On the Nature of the Tsallis–Fourier Transform
Mathematics, 2015 By recourse to tempered ultradistributions, we show here that the effect of a q-Fourier transform (qFT) is to map equivalence classes of functions into other classes in a one-to-one fashion.
A. Plastino, Mario C. Rocca
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Almost periodic generalized solutions of differential equations [PDF]
Mathematica Bohemica, 2021 The paper aims to study systems of linear ordinary differential equations in the context of an algebra of almost periodic generalized ultradistributions. Conditions on the existence of generalized solutions are given.
Chikh Bouzar, Fethia Ouikene
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Characterization of Wave Fronts of Ultradistributions Using Directional Short-Time Fourier Transform
Axioms, 2021 In this paper we give a characterization of Sobolev k-directional wave front of order p∈[1,∞) of tempered ultradistributions via the directional short-time Fourier transform.
Sanja Atanasova +2 more
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Wilson Bases and Ultradistributions
Axioms, 2021 We provide a characterization of the Gelfand–Shilov-type spaces of test functions and their dual spaces of tempered ultradistributions by means of Wilson bases of exponential decay.
Nenad Teofanov
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Boundary Values in Ultradistribution Spaces Related to Extended Gevrey Regularity
Mathematics, 2020 Following the well-known theory of Beurling and Roumieu ultradistributions, we investigate new spaces of ultradistributions as dual spaces of test functions which correspond to associated functions of logarithmic-type growth at infinity.
Stevan Pilipović +2 more
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Evolution pseudodifferential equations with analytic symbols in spaces of $S$ type
Karpatsʹkì Matematičnì Publìkacìï, 2021 A nonlocal multipoint by time problem for an evolution equation with a pseudodifferential operator is studied. This operator is treated as an infinite order differentiation operator in generalized spaces of $S$ type. We consider the case when the initial
V.V. Horodets'kyi, O.V. Martynyuk
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Asymptotically Almost Periodic Generalized Ultradistributions and Application [PDF]
Sahand Communications in Mathematical AnalysisThe paper aims to introduce and study an algebra of asymptotically almost periodic generalized ultradistributions. These generalized ultradistributions contain asymptotically almost periodic ultradistributions and asymptotically almost periodic ...
Meryem Slimani, Fethia Ouikene
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Convolution of ultradistributions and ultradistribution spaces associated to translation-invariant Banach spaces [PDF]
, 2016 We introduce and study a number of new spaces of ultradifferentiable functions and ultradistributions and we apply our results to the study of the convolution of ultradistributions.
Dimovski, Pavel +3 more
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Discrete characterizations of wave front sets of Fourier-Lebesgue and quasianalytic type [PDF]
, 2016 We obtain discrete characterizations of wave front sets of Fourier-Lebesgue and quasianalytic type. It is shown that the microlocal properties of an ultradistribution can be obtained by sampling the Fourier transforms of its localizations over a lattice ...
Debrouwere, Andreas, Vindas, Jasson
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Rotation invariant ultradistributions [PDF]
, 2017 We prove that an ultradistribution is rotation invariant if and only if it coincides with its spherical mean. For it, we study the problem of spherical representations of ultradistributions on $\mathbb{R}^{n}$. Our results apply to both the quasianalytic
Vindas Diaz, Jasson, Vuckovic, Dorde
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