For a compact subset K of the complex plane C, let C(K) denote algebra continuous functions on K. an open U?K, A(K,U)?C(K) be that are analytic in U. We show there exists ??A(K,U) so each f?A(K,U) can uniformly approximated by {pn+qn?} K, where pn and qn polynomials z. In particular, ? chosen as Cauchy transform finite positive measure ? compactly supported C?U. Recent developments capacity pro...

BACKGROUND Compressed sensing(CS) has been well applied to speed up imaging by exploring image sparsity over predefined basis functions or learnt dictionary. Firstly, the sparse representation is generally obtained in a single transform domain by using wavelet-like methods, which cannot produce optimal sparsity considering sparsity, data adaptivity and computational complexity. Secondly, most s...

We consider the transformation ev which associates to any element in a K-algebra A a function on the the set of its K-points. This is the analogue of the fundamental Gelfand transform. Both ev and its dual ev * are the maps from a discrete K-module to a topological K-module and we investigate in which case the image of each map is dense. The answer is nontrivial for various choices of K and A a...

In this article generalized attenuated ray transforms (ART) and integral angular moments are investigated. Starting from the Radon transform, transform longitudinal we derive concept of ART-operators order k over functions defined on phase space depending time. The for complex-valued absorption coefficient as well weight polynomial exponential type. Connections between ART operators various ord...

Traditionally, the special function theory has many applications in various areas of mathematical physics, economics, statistics, engineering, and other branches science. Inspired by certain recent extensions k-analogue gamma, Pochhammer symbol, hypergeometric functions, this work is devoted to study Gauss functions Hadamard product. We give a definition product k-Gauss (HPkGHF) associated with...

In this present study, we investigate the solutions for fractional kinetic equations involving k-Struve function using the Sumudu transform. The graphical interpretations of the solutions involving k-Struve function and its comparison with generalized Bessel function are given. The methodology and results can be considered and applied to various related fractional problems in mathematical physics.

Assume ψ ∈ L(R) has Fourier transform continuous at the origin, with ψ̂(0) = 1, and that ∑ l∈Zd |ψ̂(ξ − l)|2 is bounded as a function of ξ ∈ R. Then every function f ∈ L(R) can be represented by an affine series f = ∑ j>0 ∑ k∈Zd cj,kψj,k for some coefficients satisfying ‖c‖`1(`2) = ∑

Let S be a harmonic extension of an H-type group and call its modular function. We nd suucient conditions on the spherical transform of a radial distribution k on S, so that ?z k is a left resp. a right] convolutor of L p (S), 1 < p < 1, for every complex z with 0 Rez 1 resp. ?1 + 1=p Rez 1=p].

We prove a topological Paley-Wiener theorem for the Fourier transform deened on the real hyperbolic spaces SO o (p; q)=SO o (p ? 1; q), for p; q 2 2N, without restriction to K-types. We also obtain Paley-Wiener type theorems for L-Schwartz functions (0 < 2) for xed K-types.

For a range of Hardy and Bergman spaces X and sets of uniqueness K we show that for any functional φ ∈ X∗ there exists a sequence of measures (μn) supported on K converging weak* to φ. In particular, we consider H2 of the right half plane and obtain a Carleman–type formula for the continuous wavelet transform.