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  Subjects -> MATHEMATICS (Total: 886 journals)
    - APPLIED MATHEMATICS (72 journals)
    - GEOMETRY AND TOPOLOGY (20 journals)
    - MATHEMATICS (656 journals)
    - MATHEMATICS (GENERAL) (42 journals)
    - NUMERICAL ANALYSIS (19 journals)
    - PROBABILITIES AND MATH STATISTICS (77 journals)

MATHEMATICS (656 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 8)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 22)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 8)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 5)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 10)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 2)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 8)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Algebra and Logic     Hybrid Journal   (Followers: 4)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 3)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 9)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 1)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 19)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 2)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 1)
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 8)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 14)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 28)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 5)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 5)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 4)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)

        1 2 3 4 | Last

Journal Cover Computational Methods and Function Theory
  [SJR: 0.329]   [H-I: 5]   [0 followers]  Follow
    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1617-9447 - ISSN (Online) 2195-3724
   Published by Springer-Verlag Homepage  [2352 journals]
  • Quotients of Hyperbolic Metrics
    • Authors: David Minda
      Pages: 579 - 590
      Abstract: Abstract In this paper, precise versions of several intuitive properties of quotients of hyperbolic metrics are established. Suppose that \(\Omega _j\) is a hyperbolic region in \(\mathbb {C}_\infty = \mathbb {C}\cup \{\infty \}\) with hyperbolic metric \(\lambda _j\) , \(j=1,2\) , and \(\Omega _1 \subsetneq \Omega _2\) . First, it is shown that \(\lambda _1/ \lambda _2 \approx 1\) on compact subsets of \(\Omega _1\) that are not too close to \(\partial \Omega _1\) . Second, \(\lambda _1/ \lambda _2 \approx 1\) when z is near \((\partial \Omega _1 \;\cap \; \partial \Omega _2 ) {\setminus } F_b\) , where \(F = \partial \Omega _1 \;\cap \;\Omega _2\) and \(F_b = {{\mathrm{cl}}}(F)\;\cap \;\Omega _2\) . The main tools used in establishing these results are sharp elementary bounds for \(\lambda _1(z)/ \lambda _2(z)\) in terms of the hyperbolic distance relative to \(\Omega _2\) from z to \(\partial \Omega _1 \;\cap \;\Omega _2\) that were first established and employed in complex dynamics.
      PubDate: 2017-12-01
      DOI: 10.1007/s40315-017-0195-1
      Issue No: Vol. 17, No. 4 (2017)
       
  • A Normality Criterion Corresponding to the Defect Relations
    • Authors: Andreas Schweizer
      Pages: 591 - 601
      Abstract: Abstract Let \(\mathcal{{F}}\) be a family of meromorphic functions on a domain D. We present a quite general sufficient condition for \(\mathcal{{F}}\) to be a normal family. This criterion contains many known results as special cases. The overall idea is that certain comparatively weak conditions on \(\mathcal{{F}}\) by local arguments lead to somewhat stronger conditions, which in turn lead to even stronger conditions on the limit function g in the famous Zalcman Lemma. Ultimately, the defect relations for g force normality of \(\mathcal{{F}}\) .
      PubDate: 2017-12-01
      DOI: 10.1007/s40315-017-0196-0
      Issue No: Vol. 17, No. 4 (2017)
       
  • Criteria for Bounded Valence of Harmonic Mappings
    • Authors: Juha-Matti Huusko; María J. Martín
      Pages: 603 - 612
      Abstract: Abstract In 1984, Gehring and Pommerenke proved that if the Schwarzian derivative S(f) of a locally univalent analytic function f in the unit disk was such that \(\limsup _{ z \rightarrow 1} S(f)(z) (1- z ^2)^2 < 2\) , then there would exist a positive integer N such that f takes every value at most N times. Recently, Becker and Pommerenke have shown that the same result holds in those cases when the function f satisfies that \(\limsup _{ z \rightarrow 1} f''(z)/f'(z) \, (1- z ^2)< 1\) . In this paper, we generalize these two criteria for bounded valence of analytic functions to the cases when f is only locally univalent and harmonic.
      PubDate: 2017-12-01
      DOI: 10.1007/s40315-017-0197-z
      Issue No: Vol. 17, No. 4 (2017)
       
  • Uniqueness Theorems for Differential Polynomials Sharing a Small Function
    • Authors: Thi Hoai An Ta; Viet Phuong Nguyen
      Pages: 613 - 634
      Abstract: Abstract Consider meromorphic functions f,  g,  and \(\alpha ,\) where \(\alpha \) is a small function with respect to f and g. Let Q be a polynomial of one variable. We give suitable conditions on the degree of Q and on the number of zeros and the multiplicities of the zeros of \(Q'\) so as to be able to conclude uniqueness results if differential polynomials of the form \((Q(f))^{(k)}\) and \((Q(g))^{(k)}\) share \(\alpha \) counting multiplicities. We do not assume that Q has a large order zero, nor do we place restrictions on the zeros and poles of \(\alpha .\) Thus, our work improves on many prior results that either assume Q has a high order zero or place restrictions on the small function \(\alpha \) .
      PubDate: 2017-12-01
      DOI: 10.1007/s40315-017-0198-y
      Issue No: Vol. 17, No. 4 (2017)
       
  • Blaschke Products and Circumscribed Conics
    • Authors: Masayo Fujimura
      Pages: 635 - 652
      Abstract: Abstract We study geometrical properties of finite Blaschke products. For a Blaschke product B of degree d, let \(L_{\lambda }\) be the set of the lines tangent to the unit circle at the d preimages \( B^{-1}(\lambda ) \) . We show that the trace of the intersection points of each pair of two elements in \( L_{\lambda } \) as \( \lambda \) ranges over the unit circle forms an algebraic curve of degree at most \( d-1 \) . In case of low degree, we have more precise results. For instance, for \( d=3 \) , the trace forms a conic section. For \( d=4 \) , we provide a necessary and sufficient condition for Blaschke products whose trace include a conic section.
      PubDate: 2017-12-01
      DOI: 10.1007/s40315-017-0201-7
      Issue No: Vol. 17, No. 4 (2017)
       
  • The Inverse of a $$\sigma (z)$$ σ ( z ) -Harmonic Diffeomorphism
    • Authors: Hu Chunying; Shi Qingtian
      Pages: 653 - 662
      Abstract: Abstract A new kind of functional, analogous to the Douglas–Dirichlet functional, is defined as $$\begin{aligned} E'[f]=\displaystyle \iint _{\Omega }\sigma (z)( f_{z} ^{2}+ f_{\overline{z}} ^{2})\mathrm{d}x\mathrm{d}y \end{aligned}$$ for \(f\in {C^{2}}\) on \(\Omega \) with a conformal metric density \(\sigma (z)\) . A critical point of this new functional is said to be a \(\sigma (z)\) -harmonic mapping. We consider the harmonicity of the inverse function of a \(\sigma (z)\) -harmonic diffeomorphism and obtain a necessary and sufficient condition, which improves on the corresponding result for Euclidean harmonic mappings. In addition, a property of the inverse function of \(\rho \) -harmonic mappings is investigated and an example is given.
      PubDate: 2017-12-01
      DOI: 10.1007/s40315-017-0202-6
      Issue No: Vol. 17, No. 4 (2017)
       
  • A Note on the Kirwan’s Conjecture
    • Authors: Yuk-J. Leung
      Pages: 663 - 678
      Abstract: Abstract We continue our investigation on a second variation formula of the Koebe function in the class \(\Sigma \) of functions analytic and univalent in the exterior of the unit disk. Our aim is to give some supporting evidence of a conjecture raised by William Kirwan on the coefficients of functions in this class.
      PubDate: 2017-12-01
      DOI: 10.1007/s40315-017-0204-4
      Issue No: Vol. 17, No. 4 (2017)
       
  • Bohr Inequality for Odd Analytic Functions
    • Authors: Ilgiz R Kayumov; Saminathan Ponnusamy
      Pages: 679 - 688
      Abstract: Abstract We determine the Bohr radius for the class of odd functions f satisfying \( f(z) \le 1\) for all \( z <1\) , solving the recent problem of Ali et al. (J Math Anal Appl 449(1):154–167, 2017). In fact, we solve this problem in a more general setting. Then we discuss Bohr’s radius for the class of analytic functions g, when g is subordinate to a member of the class of odd univalent functions.
      PubDate: 2017-12-01
      DOI: 10.1007/s40315-017-0206-2
      Issue No: Vol. 17, No. 4 (2017)
       
  • Hardy-Type Spaces Arising from a Vector-Valued Cauchy Kernel
    • Authors: Jerry R. Muir
      Pages: 715 - 733
      Abstract: Abstract An integral formula of Cauchy type was recently developed that reproduces any continuous \(f:\overline{{\mathbb {B}}} \rightarrow {\mathbb {C}}^n\) that is holomorphic in the open unit ball \({\mathbb {B}}\) of \({\mathbb {C}}^n\) using a fixed vector-valued kernel and the scalar expression \(\langle f(u),u \rangle \) , where \(u\in \partial {\mathbb {B}}\) and \(\langle \cdot ,\cdot \rangle \) is the Hermitian inner product in \({\mathbb {C}}^n\) , which is key to defining the numerical range of f. We consider Hardy-type spaces associated with this vector-valued kernel. In particular, we introduce spaces of vector-valued holomorphic mappings properly containing the vector-valued Hardy spaces that are reproduced through the process described above and isomorphic spaces of scalar-valued non-holomorphic functions that satisfy many of the familiar properties of Hardy space functions. In the spirit of providing a straightforward introduction to these spaces, proof techniques have been kept as elementary as possible. In particular, the theory of maximal functions and singular integrals is avoided.
      PubDate: 2017-12-01
      DOI: 10.1007/s40315-017-0203-5
      Issue No: Vol. 17, No. 4 (2017)
       
  • The Bergman Analytic Content of Planar Domains
    • Authors: Matthew Fleeman; Erik Lundberg
      Pages: 369 - 379
      Abstract: Abstract Given a planar domain \(\Omega \) , the Bergman analytic content measures the \(L^{2}(\Omega )\) -distance between \(\bar{z}\) and the Bergman space \(A^{2}(\Omega )\) . We compute the Bergman analytic content of simply connected quadrature domains with quadrature formula supported at one point, and we also determine the function \(f \in A^2(\Omega )\) that best approximates \(\bar{z}\) . We show that, for simply connected domains, the square of the Bergman analytic content is equivalent to torsional rigidity from classical elasticity theory, while for multiply connected domains these two domain constants are not equivalent in general.
      PubDate: 2017-09-01
      DOI: 10.1007/s40315-016-0189-4
      Issue No: Vol. 17, No. 3 (2017)
       
  • Approximation with Rational Interpolants in $$A^{-\infty }(D)$$ A - ∞ (
           D ) for Dini Domains
    • Authors: Anders Gustafsson
      Pages: 381 - 394
      Abstract: Abstract Let D denote a Dini domain in \(\mathbb {C}\) and let \(\overline{\mathbb {C}}=\mathbb {C}\cup \{\infty \}\) . For each \(n=1,2,3\ldots \) , take points \(A_n=\{a_{ni}\}_{i=0}^n\) in D and points \(B_n=\{b_{ni}\}_{i=1}^n\) in \(\overline{\mathbb {C}}{\setminus } D\) . Let \(\alpha _n\) and \(\beta _n\) be the normalized point counting measures of \(A_n\) and \(B_n\) . Suppose that \(\alpha _n\xrightarrow {w^*}\alpha \) , \(\beta _n\xrightarrow {w^*}\beta \) and denote by \(\alpha '\) and \(\beta '\) their swept measures onto \(\partial D\) . Denote by \(U_\mu \) the logarithmic potential of the measure \(\mu \) . We show that if \(\alpha '=\beta '\) and if \(\{(n+1)(U_{\alpha _n}-U_\alpha )\}\) , \(\{n(U_{\beta _n'}-U_{\beta '})\}\) uniformly have at most logarithmic growth at \(\partial D\) , then for every \(f\in A^{-\infty }(D)\) and for the rational interpolants \(r_{n,f}\) of degree n with poles at \(B_n\) interpolating to f at \(A_n\) , we have \(r_{n,f}\rightarrow f\) in \(A^{-\infty }(D)\) .
      PubDate: 2017-09-01
      DOI: 10.1007/s40315-016-0187-6
      Issue No: Vol. 17, No. 3 (2017)
       
  • Meromorphic Functions Sharing Three Values with their Difference Operators
    • Authors: Feng Lü; Weiran Lü
      Pages: 395 - 403
      Abstract: Abstract In this work, we focus on a conjecture on the uniqueness problem of meromorphic functions sharing three distinct values with their difference operators, which is mentioned in Chen and Yi (Results Math 63, 557–565, 2013). We prove that the conjecture is true for meromorphic functions of finite order. Furthermore, a result of Zhang and Liao (Sci China Math 57, 2143–2152, 2014) is generalized from entire functions to meromorphic functions.
      PubDate: 2017-09-01
      DOI: 10.1007/s40315-016-0188-5
      Issue No: Vol. 17, No. 3 (2017)
       
  • Some Results on the Rational Bernstein–Markov Property in the
           Complex Plane
    • Authors: Federico Piazzon
      Pages: 405 - 443
      Abstract: Abstract The Bernstein–Markov property is an asymptotic quantitative assumption on the growth of uniform norms of polynomials or rational functions on a compact set with respect to \(L^2_\mu \) -norms, where \(\mu \) is a positive finite measure. We consider two variants of the Bernstein–Markov property for rational functions with restricted poles and compare them with the polynomial Bernstein–Markov property to find some sufficient conditions for the latter to imply the former. Moreover, we recover a sufficient mass-density condition for a measure to satisfy the rational Bernstein–Markov property on its support. Finally we present, as an application, a meromorphic \(L^2\) version of the Bernstein–Walsh Lemma.
      PubDate: 2017-09-01
      DOI: 10.1007/s40315-017-0194-2
      Issue No: Vol. 17, No. 3 (2017)
       
  • Angular Derivatives for Holomorphic Self-Maps of the Disk
    • Authors: Jochen Becker; Christian Pommerenke
      Pages: 487 - 497
      Abstract: Abstract Let the function \(\varphi \) be holomorphic in the unit disk \(\mathbb {D}\) and let \(\varphi (\mathbb {D})\subset \mathbb {D}\) . We consider points \(\zeta \in \partial \mathbb {D}\) where \(\varphi \) has an angular limit \(\varphi (\zeta )\in \partial \mathbb {D}\) and study the behaviour of \((\varphi (z)-\varphi (\zeta ))/(z-\zeta )\) as z tends to \(\zeta \) in various ways. In particular, there is a result connecting \( \varphi '(\zeta _{\nu }) \) and \( \varphi (\zeta _{\mu })-\varphi (\zeta _{\nu }) \) for three points \(\zeta _{\nu }\) . Expressed as a positive semidefinite quadratic form, this result could, perhaps, be generalized to n points \(\zeta _{\nu }\) .
      PubDate: 2017-09-01
      DOI: 10.1007/s40315-017-0199-x
      Issue No: Vol. 17, No. 3 (2017)
       
  • Birkhoff–James Orthogonality and the Zeros of an Analytic Function
    • Authors: Raymond Cheng; Javad Mashreghi; William T. Ross
      Pages: 499 - 523
      Abstract: Abstract Bounds are obtained for the zeros of an analytic function on a disk in terms of the Taylor coefficients of the function. These results are derived using the notion of Birkhoff–James orthogonality in the sequence space \(\ell ^p\) with \(p \in (1, \infty )\) , along with an associated Pythagorean theorem. It is shown that these methods are able to reproduce, and in some cases sharpen, some classical bounds for the roots of a polynomial.
      PubDate: 2017-09-01
      DOI: 10.1007/s40315-017-0191-5
      Issue No: Vol. 17, No. 3 (2017)
       
  • Root Sets of Polynomials and Power Series with Finite Choices of
           Coefficients
    • Authors: Simon Baker; Han Yu
      Abstract: Abstract Given \(H\subseteq \mathbb {C}\) two natural objects to study are the set of zeros of polynomials with coefficients in H, $$\begin{aligned} \left\{ z\in \mathbb {C}: \exists k>0,\, \exists (a_n)\in H^{k+1}, \sum _{n=0}^{k}a_{n}z^n=0\right\} , \end{aligned}$$ and the set of zeros of a power series with coefficients in H, $$\begin{aligned} \left\{ z\in \mathbb {C}: \exists (a_n)\in H^{\mathbb {N}}, \sum _{n=0}^{\infty } a_nz^n=0\right\} . \end{aligned}$$ In this paper, we consider the case where each element of H has modulus 1. The main result of this paper states that for any \(r\in (1/2,1),\) if H is \(2\cos ^{-1}(\frac{5-4 r ^2}{4})\) -dense in \(S^1,\) then the set of zeros of polynomials with coefficients in H is dense in \(\{z\in {\mathbb {C}}: z \in [r,r^{-1}]\},\) and the set of zeros of power series with coefficients in H contains the annulus \(\{z\in \mathbb {C}: z \in [r,1)\}\) . These two statements demonstrate quantitatively how the set of polynomial zeros/power series zeros fill out the natural annulus containing them as H becomes progressively more dense.
      PubDate: 2017-10-09
      DOI: 10.1007/s40315-017-0215-1
       
  • Brück Conjecture and Linear Differential Polynomials
    • Authors: Indrajit Lahiri; Shubhashish Das
      Abstract: Abstract In the paper we prove a uniqueness theorem for meromorphic functions that share a function of slower growth with linear differential polynomials. Our result is closely related to a conjecture of Brück.
      PubDate: 2017-10-05
      DOI: 10.1007/s40315-017-0214-2
       
  • Erratum to: On the Characterisations of a New Class of Strong Uniqueness
           Polynomials Generating Unique Range Sets
    • Authors: Abhijit Banerjee; Sanjay Mallick
      PubDate: 2017-07-29
      DOI: 10.1007/s40315-017-0211-5
       
  • Radially Distributed Values of Holomorphic Curves
    • Authors: Nan Wu
      Abstract: Abstract Using the spread relation we investigate the growth of transcendental holomorphic curves when they have radially distributed small holomorphic curves.
      PubDate: 2017-06-26
      DOI: 10.1007/s40315-017-0208-0
       
  • Fast and Accurate Computation of the Logarithmic Capacity of Compact Sets
    • Authors: Jörg Liesen; Olivier Sète; Mohamed M. S. Nasser
      Abstract: Abstract We present a numerical method for computing the logarithmic capacity of compact subsets of \(\mathbb {C}\) , which are bounded by Jordan curves and have finitely connected complement. The subsets may have several components and need not have any special symmetry. The method relies on the conformal map onto lemniscatic domains and, computationally, on the solution of a boundary integral equation with the Neumann kernel. Our numerical examples indicate that the method is fast and accurate. We apply it to give an estimate of the logarithmic capacity of the Cantor middle third set and generalizations of it.
      PubDate: 2017-06-22
      DOI: 10.1007/s40315-017-0207-1
       
 
 
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