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Microlocal analysis for Gelfand–Shilov spaces
We introduce an anisotropic global wave front set of Gelfand–Shilov ultradistributions with different indices for regularity and decay at infinity....
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Cosine Manifestations of the Gelfand Transform
The goal of the paper is to provide a detailed explanation on how the (continuous) cosine transform and the discrete(-time) cosine transform arise...
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Inversion Problem for Radon Transforms Defined on Pseudoconvex Sets
AbstractSome questions concerning the inversion of the classical and generalized integral Radon transforms are discussed. The main issue is to...
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Further Quaternion Integral Transforms
As may be expected the modification of the QFT to a localized QWT only formed the beginning of a rich field of novel quaternionic integral...
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Commutative Toeplitz Algebras and Their Gelfand Theory: Old and New Results
We present a survey and new results on the construction and Gelfand theory of commutative Toeplitz algebras over the standard weighted Bergman and...
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The Zak Transform on Gelfand–Shilov and Modulation Spaces with Applications to Operator Theory
We characterize Gelfand–Shilov spaces, their distribution spaces and modulation spaces in terms of estimates of their Zak transforms. We use these...
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Alcove Paths and Gelfand–Tsetlin Patterns
In their study of the equivariant K-theory of the generalized flag varieties G / P , where G is a complex semisimple Lie group, and P is a parabolic...
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Discrete Wavelet Transforms in Walsh Analysis
A review of discrete wavelet transforms defined through Walsh functions and used for image processing, compression of fractal signals, analysis of...
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The gyrator transform of the generalized functions
The gyrator transform is an integral transform that has attracted much attention in the field of optics and other engineering fields. We consider the...
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Linear Recursions for Integer Point Transforms
We consider the integer point transform $$\sigma _P (\mathbf {x}) = \sum _{\mathbf...
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Riesz Potentials and Orthogonal Radon Transforms on Affine Grassmannians
We establish intertwining relations between Riesz potentials associated with fractional powers of minus-Laplacian and orthogonal Radon transforms R j , k ...
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Tensor products for Gelfand–Shilov and Pilipović distribution spaces
We show basic properties on tensor products for Gelfand–Shilov distributions and Pilipović distributions. This also includes the Fubini’s property of...
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Multiresolution expansions and wavelets in Gelfand–Shilov spaces
We study approximation properties generated by highly regular scaling functions and orthonormal wavelets. These properties are conveniently described...
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Hyperbolic Systems in Gelfand and Shilov Spaces
For systems hyperbolic in Shilov’s sense whose coefficients are continuous functions of time, we study the properties of the Green function in S -type...
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mu-Brownian Motion, Dualities, Diffusions, Transforms, and Reproducing Kernel Hilbert Spaces
Replacing the Lebesgue measure on an interval by a Stieltjes positive non-atomic measure, we study the corresponding counterpart of the Brownian...