Results 41 to 50 of about 987 (103)

An Introduction to Extended Gevrey Regularity

Axioms
Gevrey classes are the most common choice when considering the regularities of smooth functions that are not analytic. However, in various situations, it is important to consider smoothness properties that go beyond Gevrey regularity, for example, when ...
Nenad Teofanov, Filip Tomić, Milica Žigić   +2 more
doaj   +1 more source

Multipliers and operators on the tempered ultradistribution spaces of Roumieu type for the distributional Hankel‐type transformation spaces

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

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

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

Weakly hyperbolic equations with non-analytic coefficients and lower order terms [PDF]

, 2012
In this paper we consider weakly hyperbolic equations of higher orders in arbitrary dimensions with time-dependent coefficients and lower order terms. We prove the Gevrey well-posedness of the Cauchy problem under $C^k$-regularity of coefficients of the ...
Garetto, Claudia, Ruzhansky, Michael
core   +3 more sources

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, Kim, Dohan, Chung, Soon-Yeong   +2 more
openaire   +2 more sources

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, Georg Zimmermann, Hans Feichtinger   +2 more
wiley   +1 more source

A projective description of generalized Gelfand-Shilov spaces of Roumieu type

, 2019
We provide a projective description for a class of generalized Gelfand-Shilov spaces of Roumieu type. In particular, our results apply to the classical Gelfand-Shilov spaces and weighted $L^\infty$-spaces of ultradifferentiable functions of Roumieu type ...
Debrouwere, Andreas, Vindas, Jasson
core   +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., Marchiano, P., Rocca, M. C.   +2 more
core   +2 more sources