An algebraic approach to tempered ultradistributions
type: Item
instance of: scholarly article
title: An algebraic approach to tempered ultradistributions
zbMATH Open document ID: 1400.46033
author: Smiljana Jakšić
author: Snjezana Maksimović
author: Stevan Pilipović
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-06-28T00:00:00Z
review text: The presentation of an isomorphism between the space of tempered distributions and that of pseudo-quotients associated with their convergence structures in [\textit{D.~Atanasiu} et al., J. Math. Anal. Appl. 384, No.~2, 307--319 (2011; Zbl 1230.42013)] inspired the authors to furnish such a result for the Beurling tempered ultradistribution spaces. The theme of the system of investigation remains the same as that in [loc. cit.], however, the analysis made to obtain the results is entirely different in the sense that in this paper an intrinsic analysis of a class of ultradistributional operators is employed instead. Let \(M\) denote the space of all functions of sub-exponential growth, which is a vector space closed under multiplication by ultrapolynomials of the form given by Equation (1.4) in the paper. An estimation for \(M_p\) polynomials is given later.
reviewed by: Deshna Loonker
Mathematics Subject Classification ID: 46F05
zbMATH DE Number: 6897102
zbMATH Keywords: pseudo-quotients
zbMATH Keywords: ultradifferentiable functions of ultrapolynomial growth
zbMATH Keywords: Beurling tempered ultradistributions
zbMATH Keywords: ultradifferential operators
MaRDI profile type: Publication
full work available at URL: j.jmaa.2018.06.033
OpenAlex ID: W2808869709
cites work: An algebraic approach to tempered distributions
cites work: Q3594582
cites work: Q5673937
cites work: A sequential approach to ultradistribution spaces
cites work: Characterizations of Bounded Sets in Spaces of Ultradistributions
DOI: 10.1016/J.JMAA.2018.06.033
description: scientific article; zbMATH DE number 6897102