Results 21 to 30 of about 105 (96)

Unified Treatment of the Krätzel Transformation for Generalized Functions

Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013
We discuss a generalization of the Krätzel transforms on certain spaces of ultradistributions. We have proved that the Krätzel transform of an ultradifferentiable function is an ultradifferentiable function and satisfies its Parseval′s inequality. We also provide a complete reading of the transform constructing two desired spaces of Boehmians.
S. K. Q. Al-Omari, A. Kılıçman, Mustafa Bayram   +2 more
wiley   +1 more source

On a class of ultradifferentiable functions

Novi Sad Journal of Mathematics, 2015
Summary: We introduce a class of ultradifferentiable functions which contains Gevrey functions and study its basic properties. In particular, we investigate the continuity properties of certain (ultra)differentiable operators. Finally, we discuss microlocal properties in appropriate dual spaces.
Pilipović, Stevan, Teofanov, Nenad, Tomić, Filip   +2 more
openaire   +1 more source

On q‐Gevrey Asymptotics for Singularly Perturbed q‐Difference‐Differential Problems with an Irregular Singularity

Abstract and Applied Analysis, Volume 2012, Issue 1, 2012., 2012
We study a q‐analog of a singularly perturbed Cauchy problem with irregular singularity in the complex domain which generalizes a previous result by Malek in (2011). First, we construct solutions defined in open q‐spirals to the origin. By means of a q‐Gevrey version of Malgrange‐Sibuya theorem we show the existence of a formal power series in the ...
Alberto Lastra, Stéphane Malek, Allan C. Peterson   +2 more
wiley   +1 more source

Inégalité de Markov en plusieurs variables

International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006
L′inégalité de Markov joue un rôle important en théorie constructive de fonctions. Dans les deux dernières décennies, on a développé sa théorie multidimensionnelle. Le but de cet article est de présenter le récent progrès de cette belle théorie.Markov′s inequality plays an important role in constructive function theory.
Wiesław Pleśniak
wiley   +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

Gelfand–Shilov Spaces for Extended Gevrey Regularity

Axioms
We consider spaces of smooth functions obtained by relaxing Gevrey-type regularity and decay conditions. It is shown that these classes can be introduced by using the general framework of the weighted matrices approach to ultradifferentiable functions ...
Nenad Teofanov, Filip Tomić, Milica Žigić   +2 more
doaj   +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

Global pseudodifferential operators in spaces of ultradifferentiable functions [PDF]

, 2021
[ES] En esta tesis estudiamos operadores pseudodiferenciales, que son operadores integrales de la forma f 7→ ∫ Rd (∫ Rd ei(x−y)·ξa(x,y,ξ)f(y)dy)dξ, en las clases globales de funciones ultradiferenciables de tipo Beurling Sω(Rd) introducidas por Björck, cuando la función peso ω viene dada en el sentido de Braun, Meise y Taylor.
openaire   +2 more sources

On scalar type spectral operators, infinite differentiable and Gevrey ultradifferentiable C0‐semigroups

International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 45, Page 2401-2422, 2004., 2004
Necessary and sufficient conditions for a scalar type spectral operator in a Banach space to be a generator of an infinite differentiable or a Gevrey ultradifferentiable C0‐semigroup are found, the latter formulated exclusively in terms of the operator′s spectrum.
Marat V. Markin
wiley   +1 more source

Ultradifferentiable functions on lines in ℝⁿ [PDF]

Proceedings of the American Mathematical Society, 1999
It is well known that a function f ∈ C ∞ ( R n ) f\in C^{\infty }(\mathbb {R}^{n}) whose restriction to every line in R n ...
openaire   +1 more source