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 Analysis in Theory and Applications   [1 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 1573-8175 - ISSN (Online) 1672-4070    Published by Springer-Verlag  [2352 journals]
• Generalized wavelets and inversion of the radon transform on the laguerre
hypergroup
• Authors: Bai Linglan; He Jianxun
Pages: 48 - 62
Abstract: Abstract Let X=R + n ×R denote the underlying manifold of polyradial functions on the Heisenberg group Hn. We construct a generalized translation on X=R + n ×R, and establish the Plancherel formula on L2(X, dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.
PubDate: 2013-09-18
DOI: 10.1007/bf02845274
Issue No: Vol. 18, No. 4 (2013)

• A regularization method for approximating the inverse Laplace transform
• Authors: A. Al-Shuaibi
Pages: 58 - 65
Abstract: Abstract A new method for approximating the inerse Laplace transform is presented. We first change our Laplace transform equation into a convolution type integral equation, where Tikhonov regularization techniques and the Fourier transformation are easily applied. We finally obtain a regularized approximation to the inverse Laplace transform as finite sum $$f\left( t \right) \cong \sum\limits_{b \approx 0}^N {b_k \left( \alpha \right)\frac{{d^h G\left( x \right)}} {{dx^h }}}$$ , where bk(a) are precalculated and tabulated regularization coefficients, G(x)=ex(ex) and g(x) is the given Laplace transform of f(t). Error bounds together with an algorithm to calculate the coefficients bk (a) and some examples are also discussed. Perturbed data problems are not included.
PubDate: 2013-09-18
DOI: 10.1007/bf02836897
Issue No: Vol. 13, No. 1 (2013)

• Some results on topical functions and upward sets
• Authors: H. Hosni; M. R. Haddai; H. Mazaheri
Pages: 301 - 308
Abstract: Abstract The purpose of this paper is to introduce and discuss the concept of topical functions on upward sets. We give characterizations of topical functions in terms of upward sets.
PubDate: 2011-12-01
DOI: 10.1007/s10496-011-0301-6
Issue No: Vol. 27, No. 4 (2011)

• The boundedness of Toeplitz-type Operators on vanishing-morrey spaces
• Authors: Xiaoniu Cao; Dongxiang Chen
Pages: 309 - 319
Abstract: Abstract In this note, we prove that the Toeplitz-type Operator Θ α b generated by the generalized fractional integral, Calderón-Zygmund operator and VMO funtion is bounded from L p,λ (R n ) to L q,µ(R n ). We also show that under some conditions Θ α b f ∈ VL q, µ(B R ), the vanishing-Morrey space.
PubDate: 2011-12-01
DOI: 10.1007/s10496-011-0309-y
Issue No: Vol. 27, No. 4 (2011)

• Almost homomorphisms between unital C*-algebras: A fixed point approach
• Authors: M. Eshaghi Gordji; S. Kaboli Gharetapeh; M. Bidkham; T. Karimi; M. Aghaei
Pages: 320 - 331
Abstract: Abstract Let A,B be two unital C*-algebras. By using fixed pint methods, we prove that every almost unital almost linear mapping h: A → B which satisfies h(2 n uy)= h(2 n u)h(y) for all u ∈ U(A), all y ∈ A, and all n=0,1,2, …, is a homomorphism. Also, we establish the generalized Hyers-Ulam-Rassias stability of *-homomorphisms on unital C*-algebras.
PubDate: 2011-12-01
DOI: 10.1007/s10496-011-0320-3
Issue No: Vol. 27, No. 4 (2011)

• A simple proof of the chaoticity of shift map under a new definition of
chaos
• Authors: Indranil Bhaumik; Binayak S. Choudhury; Basudeb Mukhopadhyay
Pages: 332 - 339
Abstract: Abstract Recently, Du has given a new strong definition of chaos by using the shift map. In this paper, we give a proof of the main theorem by constructing a dense uncountable invariant subset of the symbol space Σ2 containing transitive points in a simpler way with the help of a different metric. We also provide two examples, which support this new definition.
PubDate: 2011-12-01
DOI: 10.1007/s10496-011-0332-z
Issue No: Vol. 27, No. 4 (2011)

• Some integral inequalities for the polar derivative of a polynomial
• Authors: Abdullah Mir; Sajad Amin Baba
Pages: 340 - 350
Abstract: Abstract If P(z) is a polynomial of degree n which does not vanish in z < 1, then it is recently proved by Rather [Jour. Ineq. Pure and Appl. Math., 9 (2008), Issue 4, Art. 103] that for every γ> 0 and every real or complex number α with α ≥ 1, $\begin{gathered} \left\{ {\int_0^{2\pi } {\left {D_\alpha P(e^{i\theta } )} \right ^\gamma d\theta } } \right\}^{{1 \mathord{\left/ {\vphantom {1 \gamma }} \right. \kern-\nulldelimiterspace} \gamma }} \leqslant n( \alpha + 1)C_\gamma \left\{ {\int_0^{2\pi } {\left {P(e^{i\theta } )} \right ^\gamma d\theta } } \right\}^{{1 \mathord{\left/ {\vphantom {1 \gamma }} \right. \kern-\nulldelimiterspace} \gamma }} , \hfill \\ C_\gamma \left\{ {\frac{1} {{2\pi }}\int_0^{2\pi } {\left {1 + e^{i\beta } } \right ^\gamma d\beta } } \right\}^{ - {1 \mathord{\left/ {\vphantom {1 \gamma }} \right. \kern-\nulldelimiterspace} \gamma }} \hfill \\ \end{gathered}$ where D α P(z) denotes the polar derivative of P(z) with respect to α. In this paper we prove a result which not only provides a refinement of the above inequality but also gives a result of Aziz and Dawood [J. Approx. Theory, 54 (1988), 306–313] as a special case.
PubDate: 2011-12-01
DOI: 10.1007/s10496-011-0340-z
Issue No: Vol. 27, No. 4 (2011)

• On double sine and cosine transforms, Lipschitz and Zygmund classes
• Authors: Vanda Fülöp; Ferenc Móricaz
Pages: 351 - 364
Abstract: Abstract We consider complex-valued functions f ∈ L 1(R + 2 ), where R +:= [0,∞), and prove sufficient conditions under which the double sine Fourier transform $\hat f_{ss}$ and the double cosine Fourier transform $\hat f_{cc}$ belong to one of the two-dimensional Lipschitz classes Lip(α, β) for some 0 < α, β ≤ 1; or to one of the Zygmund classes Zyg(α, β) for some 0 < α, β ≤ 2. These sufficient conditions are best possible in the sense that they are also necessary for nonnegative-valued functions f ∈ L 1(R + 2 ).
PubDate: 2011-12-01
DOI: 10.1007/s10496-011-0351-9
Issue No: Vol. 27, No. 4 (2011)

• Boundedness of commutators for Marcinkiewicz integrals on weighted
Herz-type Hardy spaces
• Authors: Cuilan Wu
Pages: 365 - 376
Abstract: Abstract In this paper, the authors study the boundedness of the operator µ Ω b , the commutator generated by a function b ∈ Lip β (R n )(0 < β < 1) and the Marcinkiewicz integral µΩ on weighted Herz-type Hardy spaces.
PubDate: 2011-12-01
DOI: 10.1007/s10496-011-0364-4
Issue No: Vol. 27, No. 4 (2011)

• Harmonic mappings of the hexagasket to the circle
• Authors: Donglei Tang
Pages: 377 - 386
Abstract: Abstract Harmonic mappings from the hexagasket to the circle are described in terms of boundary values and topological data. Explicit formulas are also given for the energy of the mapping. We have generalized the results in [10].
PubDate: 2011-12-01
DOI: 10.1007/s10496-011-0377-z
Issue No: Vol. 27, No. 4 (2011)

• A theoretical framework for the calculation of Hausdorff measure —
Self-similar set satisfying OSC
• Authors: Zuoling Zhou; Li Feng
Pages: 387 - 398
Abstract: Abstract A theoretical framework for the calculation of Hausdorff measure of self-similar sets satisfying OSC has been established.
PubDate: 2011-12-01
DOI: 10.1007/s10496-011-0387-x
Issue No: Vol. 27, No. 4 (2011)

• Approximation and shape-preserving properties of q-Stancu operator
• Authors: Lianying Yun; Rongwei Wang
Pages: 201 - 210
Abstract: Abstract We introduce the definition of q-Stancu operator and investigate its approximation and shape-preserving property. With the help of the sign changes of f (x) and L n = f (f,q;x) the shape-preserving property of q-Stancu operator is obtained.
PubDate: 2011-09-01
DOI: 10.1007/s10496-011-0201-9
Issue No: Vol. 27, No. 3 (2011)

• A new BLO estimate for maximal singular integral operators
• Authors: Qiquan Fang; Xianliang Shi
Pages: 211 - 219
Abstract: Abstract In this paper, we extend Hu and Zhang’s results in [2] to different case.
PubDate: 2011-09-01
DOI: 10.1007/s10496-011-0211-7
Issue No: Vol. 27, No. 3 (2011)

• Some applications of BP-theorem in approximation theory
• Authors: I. Sadeqi; R. Zarghami
Pages: 220 - 223
Abstract: Abstract In this paper we apply Bishop-Phelps property to show that if X is a Banach space and G ⊆ X is the maximal subspace so that G ⊥ = {x* ∈ X* x*(y)=0; Åy ∈ G} is an L-summand in X*, then L 1(Ω,G) is contained in a maximal proximinal subspace of L 1(Ω,X).
PubDate: 2011-09-01
DOI: 10.1007/s10496-011-0220-6
Issue No: Vol. 27, No. 3 (2011)

• Measures of weak noncompactness and fixed point theory for 1-set weakly
contractive operators on unbounded domains
• Authors: Shaoyuan Xu; Afif Ben Amar
Pages: 224 - 238
Abstract: Abstract The main purpose of this paper is to prove a collection of new fixed point theorems and existence theorems for the nonlinear operator equation F(x) =αx (α ≥ 1) for so-called 1-set weakly contractive operators on unbounded domains in Banach spaces. We also introduce the concept of weakly semi-closed operator at the origin and obtain a series of new fixed point theorems and the existence theorems for the nonlinear operator equation F(x) = αx (α ≥ 1) for such class of operators. As consequences, the main results generalize and improve the relevant results, which are obtained by O’Regan and A. Ben Amar and M. Mnif in 1998 and 2009 respectively. In addition, we get the famous fixed point theorems of Leray-Schauder, Altman, Petryshyn and Rothe type in the case of weakly sequentially continuous, 1-set weakly contractive (µ-nonexpansive) and weakly semi-closed operators at the origin and their generalizations. The main condition in our results is formulated in terms of axiomatic measures of weak compactness.
PubDate: 2011-09-01
DOI: 10.1007/s10496-011-0224-2
Issue No: Vol. 27, No. 3 (2011)

• Weighted approximation of r-monotone functions on the real line by
Bernstein operators
• Authors: Laiyi Zhu; Xiaojie Zhu; Xing Liu
Pages: 239 - 250
Abstract: Abstract In this paper, we give error estimates for the weighted approximation of r-monotone functions on the real line with Freud weights by Bernstein-type operators.
PubDate: 2011-09-01
DOI: 10.1007/s10496-011-0239-8
Issue No: Vol. 27, No. 3 (2011)

• A note on H w p -boundedness of Riesz transforms and θ -Calderón-Zygmund
operators through molecular characterization
• Authors: Luong Dang Ky
Pages: 251 - 264
Abstract: Abstract Let 0 < p ≤ 1 and w in the Muckenhoupt class A 1. Recently, by using the weighted atomic decomposition and molecular characterization, Lee, Lin and Yang[11] established that the Riesz transforms R j , j = 1,2, …,n, are bounded on H w p (R n ). In this note we extend this to the general case of weight w in the Muckenhoupt class A ∞ through molecular characterization. One difficulty, which has not been taken care in [11], consists in passing from atoms to all functions in H w p (R n ). Furthermore, the H w p -boundedness of θ-Calderón-Zygmund operators are also given through molecular characterization and atomic decomposition.
PubDate: 2011-09-01
DOI: 10.1007/s10496-011-0251-z
Issue No: Vol. 27, No. 3 (2011)

• Uniform meyer solution to the three dimensional cauchy problem for laplace
equation
• Authors: Jinru Wang; Weifang Wang
Pages: 265 - 277
Abstract: Abstract We consider the three dimensional Cauchy problem for the Laplace equation $\left\{ \begin{gathered} u_{xx} (x,y,z) + u_{yy} (x,y,z) + u_{zz} (x,y,z) = 0,x \in R,y \in R,0 < z \leqslant 1, \hfill \\ u(x,y,0) = g(x,y),x \in R,y \in R, \hfill \\ u_z (x,y,0) = 0,x \in R,y \in R, \hfill \\ \end{gathered} \right.$ where the data is given at z = 0 and a solution is sought in the region x,y ∈ R,0 < z < 1. The problem is ill-posed, the solution (if it exists) doesn’t depend continuously on the initial data. Using Galerkin method and Meyer wavelets, we get the uniform stable wavelet approximate solution. Furthermore, we shall give a recipe for choosing the coarse level resolution.
PubDate: 2011-09-01
DOI: 10.1007/s10496-011-0265-6
Issue No: Vol. 27, No. 3 (2011)

• Bmo boundedness for banach space valued singular integrals
• Authors: Chunjie Zhang
Pages: 278 - 287
Abstract: Abstract In this paper, we consider a class of Banach space valued singular integrals. The L p boundedness of these operators has already been obtained. We shall discuss their boundedness from BMO to BMO. As applications, we get BMO boundedness for the classic g-function and the Marcinkiewicz integral. Some known results are improved.
PubDate: 2011-09-01
DOI: 10.1007/s10496-011-0278-1
Issue No: Vol. 27, No. 3 (2011)

• On convergence of general Gamma type operators
• Authors: Harun Karsli
Pages: 288 - 300
Abstract: Abstract The present paper deals with the new type of Gamma operators, here we estimate the rate of pointwise convergence of these new Gamma type operators M n,k for functions of bounded variation, by using some techniques of probability theory.
PubDate: 2011-09-01
DOI: 10.1007/s10496-011-0288-z
Issue No: Vol. 27, No. 3 (2011)

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