Subjects -> MATHEMATICS (Total: 1118 journals)     - APPLIED MATHEMATICS (92 journals)    - GEOMETRY AND TOPOLOGY (23 journals)    - MATHEMATICS (819 journals)    - MATHEMATICS (GENERAL) (45 journals)    - NUMERICAL ANALYSIS (26 journals)    - PROBABILITIES AND MATH STATISTICS (113 journals) MATHEMATICS (819 journals)                  1 2 3 4 5 | Last
 Showing 1 - 200 of 538 Journals sorted alphabetically Abakós       (Followers: 5) Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg       (Followers: 3) Accounting Perspectives       (Followers: 9) ACM Transactions on Algorithms (TALG)       (Followers: 17) ACM Transactions on Computational Logic (TOCL)       (Followers: 5) ACM Transactions on Mathematical Software (TOMS)       (Followers: 9) ACS Applied Materials & Interfaces       (Followers: 44) Acta Applicandae Mathematicae       (Followers: 2) Acta Mathematica       (Followers: 11) Acta Mathematica Hungarica       (Followers: 2) Acta Mathematica Scientia       (Followers: 5) Acta Mathematica Sinica, English Series       (Followers: 6) Acta Mathematica Vietnamica Acta Mathematicae Applicatae Sinica, English Series Advanced Science Letters       (Followers: 13) Advances in Applied Clifford Algebras       (Followers: 6) Advances in Catalysis       (Followers: 8) Advances in Complex Systems       (Followers: 12) Advances in Computational Mathematics       (Followers: 23) Advances in Decision Sciences       (Followers: 4) Advances in Difference Equations       (Followers: 5) Advances in Fixed Point Theory       (Followers: 9) Advances in Geosciences (ADGEO)       (Followers: 22) Advances in Linear Algebra & Matrix Theory       (Followers: 10) Advances in Materials Science       (Followers: 22) Advances in Mathematical Physics       (Followers: 10) Advances in Mathematics       (Followers: 22) Advances in Numerical Analysis       (Followers: 8) Advances in Operations Research       (Followers: 14) Advances in Operator Theory       (Followers: 4) Advances in Porous Media       (Followers: 6) Advances in Pure Mathematics       (Followers: 11) Advances in Science and Research (ASR)       (Followers: 8) Aequationes Mathematicae       (Followers: 2) African Journal of Educational Studies in Mathematics and Sciences       (Followers: 12) African Journal of Mathematics and Computer Science Research       (Followers: 7) Afrika Matematika       (Followers: 3) Air, Soil & Water Research       (Followers: 13) AKSIOMA Journal of Mathematics Education       (Followers: 4) AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika       (Followers: 1) Al-Jabar : Jurnal Pendidikan Matematika       (Followers: 1) Al-Qadisiyah Journal for Computer Science and Mathematics       (Followers: 1) AL-Rafidain Journal of Computer Sciences and Mathematics       (Followers: 6) Algebra and Logic       (Followers: 8) Algebra Colloquium       (Followers: 4) Algebra Universalis       (Followers: 2) Algorithmic Operations Research       (Followers: 5) Algorithms       (Followers: 14) Algorithms Research       (Followers: 2) American Journal of Computational and Applied Mathematics       (Followers: 10) American Journal of Mathematical Analysis       (Followers: 2) American Journal of Mathematical and Management Sciences       (Followers: 1) American Journal of Mathematics       (Followers: 9) American Journal of Operations Research       (Followers: 8) American Mathematical Monthly       (Followers: 7) An International Journal of Optimization and Control: Theories & Applications       (Followers: 13) Analele Universitatii Ovidius Constanta - Seria Matematica Analysis and Applications       (Followers: 2) Analysis and Mathematical Physics       (Followers: 10) Analysis Mathematica Anargya : Jurnal Ilmiah Pendidikan Matematika       (Followers: 8) Annales Mathematicae Silesianae       (Followers: 2) Annales mathématiques du Québec       (Followers: 4) Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica       (Followers: 1) Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica Annali di Matematica Pura ed Applicata       (Followers: 1) Annals of Combinatorics       (Followers: 3) Annals of Data Science       (Followers: 17) Annals of Discrete Mathematics       (Followers: 8) Annals of Functional Analysis       (Followers: 4) Annals of Mathematics       (Followers: 4) Annals of Mathematics and Artificial Intelligence       (Followers: 16) Annals of PDE Annals of Pure and Applied Logic       (Followers: 6) Annals of the Alexandru Ioan Cuza University - Mathematics Annals of the Institute of Statistical Mathematics       (Followers: 1) Annals of West University of Timisoara - Mathematics       (Followers: 1) Annals of West University of Timisoara - Mathematics and Computer Science       (Followers: 2) Annuaire du Collège de France       (Followers: 6) ANZIAM Journal       (Followers: 2) Applicable Algebra in Engineering, Communication and Computing       (Followers: 3) Applications of Mathematics       (Followers: 3) Applied Categorical Structures       (Followers: 4) Applied Computational Intelligence and Soft Computing       (Followers: 16) Applied Mathematics       (Followers: 10) Applied Mathematics       (Followers: 6) Applied Mathematics & Optimization       (Followers: 13) Applied Mathematics - A Journal of Chinese Universities       (Followers: 2) Applied Mathematics and Nonlinear Sciences       (Followers: 1) Applied Mathematics Letters       (Followers: 3) Applied Mathematics Research eXpress       (Followers: 2) Applied Network Science       (Followers: 3) Applied Numerical Mathematics       (Followers: 6) Applied Spatial Analysis and Policy       (Followers: 6) Arab Journal of Mathematical Sciences       (Followers: 4) Arabian Journal of Mathematics       (Followers: 2) Archive for Mathematical Logic       (Followers: 4) Archive of Applied Mechanics       (Followers: 6) Archive of Numerical Software Archives of Computational Methods in Engineering       (Followers: 6) Arkiv för Matematik       (Followers: 1) Armenian Journal of Mathematics       (Followers: 1) Arnold Mathematical Journal       (Followers: 1) Artificial Satellites       (Followers: 24) Asia-Pacific Journal of Operational Research       (Followers: 3) Asian Journal of Algebra       (Followers: 1) Asian Research Journal of Mathematics Asian-European Journal of Mathematics       (Followers: 4) Australian Mathematics Teacher, The       (Followers: 7) Australian Primary Mathematics Classroom       (Followers: 7) Australian Senior Mathematics Journal       (Followers: 2) Automatic Documentation and Mathematical Linguistics       (Followers: 5) Axioms       (Followers: 1) Baltic International Yearbook of Cognition, Logic and Communication       (Followers: 2) Banach Journal of Mathematical Analysis       (Followers: 1) Basin Research       (Followers: 6) BIBECHANA       (Followers: 2) Biomath BIT Numerical Mathematics       (Followers: 1) Boletim Cearense de Educação e História da Matemática Boletim de Educação Matemática Boletín de la Sociedad Matemática Mexicana Bollettino dell'Unione Matematica Italiana       (Followers: 3) British Journal for the History of Mathematics British Journal of Mathematical and Statistical Psychology       (Followers: 20) Bruno Pini Mathematical Analysis Seminar Buletinul Academiei de Stiinte a Republicii Moldova. Matematica       (Followers: 15) Bulletin des Sciences Mathamatiques       (Followers: 4) Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory       (Followers: 3) Bulletin of Mathematical Sciences       (Followers: 1) Bulletin of Symbolic Logic       (Followers: 3) Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics Bulletin of the Australian Mathematical Society       (Followers: 2) Bulletin of the Brazilian Mathematical Society, New Series Bulletin of the Iranian Mathematical Society Bulletin of the London Mathematical Society       (Followers: 3) Bulletin of the Malaysian Mathematical Sciences Society Cadernos do IME : Série Matemática       (Followers: 2) Calculus of Variations and Partial Differential Equations Canadian Journal of Mathematics / Journal canadien de mathématiques Canadian Journal of Science, Mathematics and Technology Education       (Followers: 23) Canadian Mathematical Bulletin Carpathian Mathematical Publications       (Followers: 1) Catalysis in Industry       (Followers: 1) CEAS Space Journal       (Followers: 6) CHANCE       (Followers: 5) Chaos, Solitons & Fractals       (Followers: 3) Chaos, Solitons & Fractals : X       (Followers: 1) ChemSusChem       (Followers: 8) Chinese Annals of Mathematics, Series B Chinese Journal of Catalysis       (Followers: 3) Chinese Journal of Mathematics Ciencia       (Followers: 1) CODEE Journal       (Followers: 2) Cogent Mathematics       (Followers: 2) Cognitive Computation       (Followers: 3) Collectanea Mathematica College Mathematics Journal       (Followers: 4) COMBINATORICA Combinatorics, Probability and Computing       (Followers: 4) Combustion Theory and Modelling       (Followers: 18) Commentarii Mathematici Helvetici Communications in Advanced Mathematical Sciences Communications in Combinatorics and Optimization Communications in Contemporary Mathematics Communications in Mathematical Physics       (Followers: 4) Communications On Pure & Applied Mathematics       (Followers: 5) Complex Analysis and its Synergies       (Followers: 3) Complex Variables and Elliptic Equations: An International Journal Composite Materials Series       (Followers: 11) Compositio Mathematica Comptes Rendus : Mathematique Computational and Applied Mathematics       (Followers: 4) Computational and Mathematical Methods Computational and Mathematical Methods in Medicine       (Followers: 3) Computational and Mathematical Organization Theory       (Followers: 1) Computational Complexity       (Followers: 4) Computational Mathematics and Modeling       (Followers: 9) Computational Mechanics       (Followers: 10) Computational Methods and Function Theory Computational Optimization and Applications       (Followers: 11) Computers & Mathematics with Applications       (Followers: 11) Confluentes Mathematici Constructive Mathematical Analysis       (Followers: 1) Contributions to Discrete Mathematics       (Followers: 1) Contributions to Game Theory and Management COSMOS       (Followers: 1) Cryptography and Communications       (Followers: 14) Cuadernos de Investigación y Formación en Educación Matemática Cubo. A Mathematical Journal Current Research in Biostatistics       (Followers: 8) Czechoslovak Mathematical Journal       (Followers: 1) Daya Matematis : Jurnal Inovasi Pendidikan Matematika       (Followers: 1) Demographic Research       (Followers: 16) Design Journal : An International Journal for All Aspects of Design       (Followers: 35) Desimal : Jurnal Matematika       (Followers: 3) Developments in Clay Science       (Followers: 1) Developments in Mineral Processing       (Followers: 3) Dhaka University Journal of Science Differential Equations and Dynamical Systems       (Followers: 4)

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Similar Journals
 Collectanea MathematicaNumber of Followers: 0      Hybrid journal (It can contain Open Access articles) ISSN (Print) 0010-075 - ISSN (Online) 2038-4815 Published by Springer-Verlag  [2658 journals]
• Tropically planar graphs

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Abstract: We study tropically planar graphs, which are the graphs that appear in smooth tropical plane curves. We develop necessary conditions for graphs to be tropically planar, and compute the number of tropically planar graphs up to genus 7. We provide non-trivial upper and lower bounds on the number of tropically planar graphs, and prove that asymptotically $$0\%$$ of connected trivalent planar graphs are tropically planar.
PubDate: 2021-10-07

• Fourier multipliers for Triebel–Lizorkin spaces on compact Lie
groups

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Abstract: We investigate the boundedness of Fourier multipliers on a compact Lie group when acting on Triebel-Lizorkin spaces. Criteria are given in terms of the Hörmander-Mihlin-Marcinkiewicz condition. In our analysis, we use the difference structure of the unitary dual of a compact Lie group. Our results cover the sharp Hörmander-Mihlin theorem on Lebesgue spaces and also other historical results on the subject.
PubDate: 2021-10-06

• Equilibrium measures on trees

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Abstract: We give a characterization of equilibrium measures for p-capacities on the boundary of an infinite tree of arbitrary (finite) local degree. For $$p=2$$ , this provides, in the special case of trees, a converse to a theorem of Benjamini and Schramm, which interpretes the equilibrium measure of a planar graph’s boundary in terms of square tilings of cylinders.
PubDate: 2021-09-23

• A new concept of smoothness in Orlicz spaces

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Abstract: In a 2015 article Cuenya and Ferreyra defined a class of functions in $$L^p$$ -spaces, denoted by $$c_n^p(x)$$ . The class $$c_n^p(x)$$ contains the class of $$L^p$$ -differentiability functions, denoted by $$t_n^p(x)$$ , introduced in a 1961 article by Calderón-Zygmund. A more recent paper by Acinas, Favier and Zó introduced a new class of functions in Orlicz spaces $$L^\Phi$$ , called $$L^\Phi$$ -differentiable functions in the present article. The class of $$L^\Phi$$ -differentiable functions is closely related to the class $$t_n^p(x)$$ . In this work, we define a class of functions in $$L^\Phi$$ , denoted by $$c_n^{\Phi }(x)$$ . The class $$c_n^{\Phi }(x)$$ is more general than the class of $$L^{\varPhi}$$ -differentiable functions. We prove the existence of the best local $$\Phi$$ -approximation for functions in $$c_n^{\varPhi }(x)$$ and study the convexity of the set of cluster points of the set of best $$\Phi$$ -approximations to a function on an interval when their measures tend to zero.
PubDate: 2021-09-17

• Some results concerning ideal and classical uniform integrability and mean
convergence

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Abstract: In this article, the concept of $${\mathcal {J}}$$ -uniform integrability of a sequence of random variables $$\left\{ X_{k}\right\}$$ with respect to $$\left\{ a_{nk} \right\}$$ is introduced where $${\mathcal {J}}$$ is a non-trivial ideal of subsets of the set of positive integers and $$\left\{ a_{nk} \right\}$$ is an array of real numbers. We show that this concept is weaker than the concept of $$\left\{ X_{k} \right\}$$ being uniformly integrable with respect to $$\left\{ a_{nk} \right\}$$ and is more general than the concept of B-statistical uniform integrability with respect to $$\left\{ a_{nk} \right\}$$ . We give two characterizations of $${\mathcal {J}}$$ -uniform integrability with respect to $$\left\{ a_{nk} \right\}$$ . One of them is a de La Vallée Poussin type characterization. For a sequence of pairwise independent random variables $$\left\{ X_{k} \right\}$$ which is $${\mathcal {J}}$$ -uniformly integrable with respect to $$\left\{ a_{nk} \right\}$$ , a law of large numbers with mean ideal convergence is proved. We also obtain a version without the pairwise independence assumption by strengthening other conditions. Supplements to the classical Mean Convergence Criterion are also established.
PubDate: 2021-09-16

• Sparse domination results for compactness on weighted spaces

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Abstract: By means of appropriate sparse bounds, we deduce compactness on weighted $$L^p(w)$$ spaces, $$1<p<\infty$$ , for all Calderón–Zygmund operators having compact extensions on $$L^2({\mathbb {R}}^n)$$ . Similar methods lead to new results on boundedness and compactness of Haar multipliers on weighted spaces. In particular, we prove weighted bounds for weights in a class strictly larger than the typical $$A_p$$ class.
PubDate: 2021-09-04

• Resurgence numbers of fiber products of projective schemes

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Abstract: We investigate the resurgence and asymptotic resurgence numbers of fiber products of projective schemes. Particularly, we show that while the asymptotic resurgence number of the k-fold fiber product of a projective scheme remains unchanged, its resurgence number could strictly increase.
PubDate: 2021-09-01

• On a question of Hartshorne

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Abstract: Let I be an ideal of a commutative Noetherian ring R. It is shown that the R-modules $$H^i_I(M)$$ are I-cofinite, for all finitely generated R-modules M and all $$i\in {\mathbb {N}}_0$$ , if and only if the R-modules $$H^i_I(R)$$ are I-cofinite with dimension not exceeding 1, for all integers $$i\ge 2$$ ; in addition, under these equivalent conditions it is shown that, for each minimal prime ideal $${{\mathfrak {p}}}$$ over I, either $${{\text {height}}}{{\mathfrak {p}}}\le 1$$ or $$\dim R/{{\mathfrak {p}}}\le 1$$ , and the prime spectrum of the I-transform R-algebra $$D_I(R)$$ equipped with its Zariski topology is Noetherian. Also, by constructing an example we show that under the same equivalent conditions in general the ring $$D_I(R)$$ need not be Noetherian. Furthermore, in the case that R is a local ring, it is shown that the R-modules $$H^i_I(M)$$ are I-cofinite, for all finitely generated R-modules M and all $$i\in {\mathbb {N}}_0$$ , if and only if for each minimal prime ideal $${\mathfrak {P}}$$ of $${\widehat{R}}$$ , either $$\dim {\widehat{R}}/(I{\widehat{R}}+{\mathfrak {P}})\le 1$$ or $$H^i_{I{\widehat{R}}}({\widehat{R}}/{\mathfrak {P}})=0$$ , for all integers $$i\ge 2$$ . Finally, it is shown that if R is a semi-local ring and the R-modules $$H^i_I(M)$$ are I-cofinite, for all finitely generated R-modules M and all $$i\in {\mathbb {N}}_0$$ , then the category of all I-cofinite modules forms an Abelian subcategory of the category of all R-modules.
PubDate: 2021-09-01

• Fractional Paley–Wiener and Bernstein spaces

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Abstract: We introduce and study a family of spaces of entire functions in one variable that generalise the classical Paley–Wiener and Bernstein spaces. Namely, we consider entire functions of exponential type a whose restriction to the real line belongs to the homogeneous Sobolev space $$\dot{W}^{s,p}$$ and we call these spaces fractional Paley–Wiener if $$p=2$$ and fractional Bernstein spaces if $$p\in (1,\infty )$$ , that we denote by $$PW^s_a$$ and $${\mathcal {B}}^{s,p}_a$$ , respectively. For these spaces we provide a Paley–Wiener type characterization, we remark some facts about the sampling problem in the Hilbert setting and prove generalizations of the classical Bernstein and Plancherel–Pólya inequalities. We conclude by discussing a number of open questions.
PubDate: 2021-09-01

• Hilbert–Poincaré series of parity binomial edge ideals and permanental
ideals of complete graphs

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Abstract: We give an explicit formula for the Hilbert–Poincaré series of the parity binomial edge ideal of a complete graph  $$K_{n}$$ or equivalently for the ideal generated by all $$2\times 2$$ -permanents of a $$2\times n$$ -matrix. It follows that the depth and Castelnuovo–Mumford regularity of these ideals are independent of n.
PubDate: 2021-09-01

• Szczarba’s twisting cochain and the Eilenberg–Zilber maps

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Abstract: We show that Szczarba’s twisting cochain for a twisted Cartesian product is essentially the same as the one constructed by Shih. More precisely, Szczarba’s twisting cochain can be obtained via the basic perturbation lemma if one uses a ‘reversed’ version of the classical Eilenberg–Mac Lane homotopy for the Eilenberg–Zilber contraction. Along the way we prove several new identities involving these homotopies.
PubDate: 2021-09-01

• On the Davis-Wielandt shell of an operator and the Davis-Wielandt index of
a normed linear space

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Abstract: We study the Davis-Wielandt shell and the Davis-Wielandt radius of an operator on a normed linear space $$\mathcal {X}$$ . We show that after a suitable modification, the modified Davis-Wielandt radius defines a norm on $$\mathcal {L}(\mathcal {X})$$ which is equivalent to the usual operator norm on $$\mathcal {L}(\mathcal {X})$$ . We introduce the Davis-Wielandt index of a normed linear space and compute its value explicitly in case of some particular polyhedral Banach spaces. We also present a general method to estimate the Davis-Wielandt index of any polyhedral finite-dimensional Banach space.
PubDate: 2021-09-01

• Stone–Weierstrass theorems for Riesz ideals of continuous functions

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Abstract: Notions of convergence and continuity specifically adapted to Riesz ideals $$\mathscr {I}$$ of the space of continuous real-valued functions on a Lindelöf locally compact Hausdorff space are given, and used to prove Stone–Weierstrass-type theorems for $$\mathscr {I}$$ . As applications, sufficient conditions are discussed that guarantee that various types of positive linear maps on $$\mathscr {I}$$ are uniquely determined by their restriction to various point-separating subsets of $$\mathscr {I}$$ . A very special case of this is the characterization of the strong determinacy of moment problems, which is rederived here in a rather general setting and without making use of spectral theory.
PubDate: 2021-09-01

• Duality of gauges and symplectic forms in vector spaces

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Abstract: A gauge $$\gamma$$ in a vector space X is a distance function given by the Minkowski functional associated to a convex body K containing the origin in its interior. Thus, the outcoming concept of gauge spaces $$(X, \gamma )$$ extends that of finite dimensional real Banach spaces by simply neglecting the symmetry axiom (a viewpoint that Minkowski already had in mind). If the dimension of X is even, then the fixation of a symplectic form yields an identification between X and its dual space $$X^*$$ . The image of the polar body $$K^{\circ }\subseteq X^*$$ under this identification yields a (skew-)dual gauge on X. In this paper, we study geometric properties of this so-called dual gauge, such as its behavior under isometries and its relation to orthogonality. A version of the Mazur–Ulam theorem for gauges is also proved. As an application of the theory, we show that closed characteristics of the boundary of a (smooth) convex body are optimal cases of a certain isoperimetric inequality.
PubDate: 2021-09-01

• Orlicz spaces associated to a quasi-Banach function space: applications to
vector measures and interpolation

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Abstract: The Orlicz spaces $$X^{\varPhi }$$ associated to a quasi-Banach function space X are defined by replacing the role of the space $$L^1$$ by X in the classical construction of Orlicz spaces. Given a vector measure m,  we can apply this construction to the spaces $$L^1_w(m),$$ $$L^1(m)$$ and $$L^1(\Vert m\Vert )$$ of integrable functions (in the weak, strong and Choquet sense, respectively) in order to obtain the known Orlicz spaces $$L^{\varPhi }_w(m)$$ and $$L^{\varPhi }(m)$$ and the new ones $$L^{\varPhi }(\Vert m\Vert ).$$ Therefore, we are providing a framework where dealing with different kind of Orlicz spaces in a unified way. Some applications to complex interpolation are also given.
PubDate: 2021-09-01

• Oscillations on one dimensional time dependent center manifolds: algebraic
curves approach

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Abstract: We consider a one dimensional time dependent ODE of degree $$n\ge 2$$ as the restriction of an arbitrary nonautonomous ODE to the associated one dimensional center manifold. Then, we present an algorithm for computing time dependent algebraic curves of m-th degree with $$m\le n-1$$ . This computation leads us to a m dimensional time dependent bifurcation equation. We determine oscillatory behaviors of the system with the help of the bifurcation equation. Finally, we complete the method for a general parametric planar system and find periodic solutions. The method can be applied for a wide range of nonautonomous systems and does not have restrictions of classical methods such as the Poincaré map.
PubDate: 2021-08-02

• Smooth determinantal varieties and critical loci in multiview geometry

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Abstract: Linear projections from $$\mathbb {P}^k$$ to $$\mathbb {P}^h$$ appear in computer vision as models of images of dynamic or segmented scenes. Given multiple projections of the same scene, the identification of sufficiently many correspondences between the images allows, in principle, to reconstruct the position of the projected objects. A critical locus for the reconstruction problem is a variety in $$\mathbb {P}^k$$ containing the set of points for which the reconstruction fails. Critical loci turn out to be determinantal varieties. In this paper we determine and classify all the smooth critical loci, showing that they are classical projective varieties.
PubDate: 2021-07-29

• Semiregular and strongly irregular boundary points for p-harmonic
functions on unbounded sets in metric spaces

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Abstract: The trichotomy between regular, semiregular, and strongly irregular boundary points for $$p$$ -harmonic functions is obtained for unbounded open sets in complete metric spaces with a doubling measure supporting a $$p$$ -Poincaré inequality, $$1<p<\infty$$ . We show that these are local properties. We also deduce several characterizations of semiregular points and strongly irregular points. In particular, semiregular points are characterized by means of capacity, $$p$$ -harmonic measures, removability, and semibarriers.
PubDate: 2021-07-28

• Structure of the Lipschitz free p-spaces
$${\mathcal{F}}_p({\mathbb{Z}}^d)$$ F p ( Z d ) and
$${\mathcal{F}}_p({\mathbb{R}}^d)$$ F p ( R d ) for 0       p ≤ 1

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Abstract: Our aim in this article is to contribute to the theory of Lipschitz free p-spaces for $$0<p\le 1$$ over the Euclidean spaces $${\mathbb{R}}^d$$ and $${\mathbb{Z}}^d$$ . To that end, we show that $${\mathcal{F}}_p({\mathbb{R}}^d)$$ admits a Schauder basis for every $$p\in (0,1]$$ , thus generalizing the corresponding result for the case $$p=1$$ by Hájek and Pernecká (J Math Anal Appl 416(2):629–646, 2014, Theorem 3.1) and answering in the positive a question that was raised by Albiac et al. in (J Funct Anal 278(4):108354, 2020). Explicit formulas for the bases of $${\mathcal{F}}_p({\mathbb{R}}^d)$$ and its isomorphic space $${\mathcal{F}}_p([0,1]^d)$$ are given. We also show that the well-known fact that $${\mathcal{F}}({\mathbb{Z}})$$ is isomorphic to $$\ell _{1}$$ does not extend to the case when $$p<1$$ , that is, $${\mathcal{F}}_{p}({\mathbb{Z}})$$ is not isomorphic to $$\ell _{p}$$ when $$0<p<1$$ .
PubDate: 2021-07-19

• A generalized Grobman–Hartman theorem for nonautonomous dynamics

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Abstract: The purpose of this note is to extend the recent generalized version of the Grobman–Hartman theorem established by Bernardes Jr. and Messaoudi from an autonomous to nonautonomous dynamics. More precisely, we prove that any sufficiently small perturbation of a nonautonomous linear dynamics that admits a generalized exponential dichotomy is topologically conjugated to its linear part. In addition, we prove that under certain mild additional conditions, the conjugacy is in fact Hölder continuous.
PubDate: 2021-07-10

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