Results 41 to 50 of about 989 (103)
International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006 The tempered ultradistribution space of Roumieu type for the space Hμ,ν is defined, which is a subspace of the Hausdörff locally convex topological linear space. Further, results are obtained for the multipliers and operators on the tempered ultradistribution spaces for the distributional Hankel‐type transformation spaces.
P. K. Banerji, S. K. Al-Omari
wiley +1 more source
Structural theorems for periodic ultradistributions [PDF]
Proceedings of the American Mathematical Society, 1986 Structural theorems for periodic ultradistributions of Roumieu and Beurling types are given.
openaire +1 more source
The short-time Fourier transform of distributions of exponential type and Tauberian theorems for shift-asymptotics [PDF]
, 2016 We study the short-time Fourier transform on the space $\mathcal{K}_{1}'(\mathbb{R}^n)$ of distributions of exponential type. We give characterizations of $\mathcal{K}_{1}'(\mathbb{R}^n)$ and some of its subspaces in terms of modulation spaces.
Kostadinova, Sanja +3 more
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On the Fourier transform and the exchange property
International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 16, Page 2579-2584, 2005., 2005 A simplified construction of tempered Boehmians is presented. The new construction shows that considering delta sequences and convergence arguments is not essential.
Dragu Atanasiu, Piotr Mikusiński
wiley +1 more source
Convolution of Ultradistributions, Field Theory, Lorentz Invariance and Resonances [PDF]
, 2006 In this work, a general definition of convolution between two arbitrary Ultradistributions of Exponential type (UET) is given. The product of two arbitrary UET is defined via the convolution of its corresponding Fourier Transforms.
Bollini, C. G. +2 more
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Asymptotic hyperfunctions, tempered hyperfunctions, and asymptotic expansions
International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 5, Page 755-788, 2005., 2005 We introduce new subclasses of Fourier hyperfunctions of mixed type, satisfying polynomial growth conditions at infinity, and develop their sheaf and duality theory. We use Fourier transformation and duality to examine relations of these asymptotic and tempered hyperfunctions to known classes of test functions and distributions, especially the Gel′fand‐
Andreas U. Schmidt
wiley +1 more source
Bochner–Schwartz Theorems for Ultradistributions
Journal of Mathematical Analysis and Applications, 1998 Das Bochner Theorem für eine positiv definite, stetige Funktion \(f\) in \(\mathbb{R}^n\) sagt aus, dass die folgenden drei Bedingungen äquivalent sind: (1) \(f\) ist positiv definit, (2) \(f\) ist die Fourier Transformatierte eines positiven, endlichen Maßes, (3) für jede \(C^\infty\) Funktion \(\varphi\) mit kompaktem Träger gilt \[ \iint \overline{f(
Cho, Jonggyu +2 more
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Spaces of Test Functions via the STFT
Journal of Function Spaces, Volume 2, Issue 1, Page 25-53, 2004., 2004 We characterize several classes of test functions, among them Björck′s ultra‐rapidly decaying test functions and the Gelfand‐Shilov spaces of type S, in terms of the decay of their short‐time Fourier transform and in terms of their Gabor coefficients.
Karlheinz Gröchenig +2 more
wiley +1 more source
The Fractionary Schr\"{o}dinger Equation, Green Functions and Ultradistributions [PDF]
, 2010 In this work, we generalize previous results about the Fractionary Schr\"{o}dinger Equation within the formalism of the theory of Tempered Ultradistributions. Several examples of the use of this theory are given.
A.L. De Paoli +25 more
core +2 more sources
Polynomials on the space of ω-ultradifferentiable functions [PDF]
Opuscula Mathematica, 2007 The space of polynomials on the the space \(D_{\omega}\) of \(\omega\)-ultradifferentiable functions is represented as the direct sum of completions of symmetric tensor powers of \(D^{\prime}_{\omega}\).
Katarzyna Grasela
doaj