Results 1 to 10 of about 987 (103)
Wilson Bases and Ultradistributions [PDF]
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. We offer two different proofs and extend known results to the Roumieu case.
Nenad Teofanov
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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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Convolution of ultradistributions and ultradistribution spaces associated to translation-invariant Banach spaces [PDF]
Kyoto Journal of Mathematics, 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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Generalized Hermitean ultradistributions [PDF]
Mathematica Bohemica, 2009 Summary: We define, by duality methods, a space of ultradistributions \(\mathcal G _\omega ' (\mathbb R ^N)\). This space contains all tempered distributions and is closed under derivatives, complex translations and Fourier transform. Moreover, it contains some multipole series and all entire functions of order less than two.
Andrade, C., Loura, L.
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Analytic ultradistributions [PDF]
Proceedings of the American Mathematical Society, 1995 A necessary and sufficient condition that an ultradistribution, of Beurling or Roumieu type, which is defined on an open set Ω ⊂ R n \Omega \subset {\mathcal {R}^n} is a real analytic function is given.
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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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On quasianalytic classes of Gelfand-Shilov type. Parametrix and convolution [PDF]
, 2017 We develop a convolution theory for quasianalytic ultradistributions of Gelfand-Shilov type. We also construct a special class of ultrapolynomials, and use it as a base for the parametrix method in the study of new topological and structural properties ...
Pilipovic, Stevan +2 more
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A non-linear theory of infrahyperfunctions [PDF]
, 2019 We develop a nonlinear theory for infrahyperfunctions (also referred to as quasianalytic (ultra)distributions by L. H\"{o}rmander). In the hyperfunction case our work can be summarized as follows.
Debrouwere, Andreas +2 more
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Eigenfunction expansions of ultradifferentiable functions and ultradistributions in ℝⁿ [PDF]
, 2016 We obtain a characterization of ${\mathcal S}^{\{M_p\}}_{\{M_p\}}(\mathbb{R}^n)$ and $\mathcal {S}^{(M_p)}_{(M_p)}(\mathbb{R}^n)$, the general Gelfand-Shilov spaces of ultradifferentiable functions of Roumieu and Beurling type, in terms of decay ...
Vindas Diaz, Jasson, Vuckovic, Dorde
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Eigenfunction expansions of ultradifferentiable functions and ultradistributions [PDF]
, 2016 In this paper we give a global characterisation of classes of ultradifferentiable functions and corresponding ultradistributions on a compact manifold $X$.
Dasgupta, Aparajita, Ruzhansky, Michael
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