Boehmians and generalized functions
type: Item
instance of: scholarly article
title: Boehmians and generalized functions
zbMATH Open document ID: 0652.44005
DOI: 10.1007/BF01903334
published in: Acta Mathematica Hungarica
publication date: 1988-01-01T00:00:00Z
review text: This paper makes a unity with the two ones published previously by \textit{J. Mikusiński} [C. R. Acad. Sci., Paris, Sér. I 293, 463-464 (1981; Zbl 0495.44006)] and the author [Japan J. Math. 9, 159-179 (1983; Zbl 0524.44005)] and completes them. The most interesting results are given in the third part of the paper which is devoted to the convergence of Boehmians and in the last part in which the author discusses the connection between Boehmians and other generalized functions, used at the most. It is interesting that Boehmians contain all distributions. We cite only one theorem. Let G be a linear space, S subspace of G and \(\Delta\) be a family of delta sequences, then by \(B(G,\Delta)\) we denote the set of Boehmians and \(B_ F(G,\Delta)=\{f\in B(G,\Delta),f*\phi \in G,\phi \in F\},\) F is a subsemigroup of S. Theorem: ``Let F be a subalgebra of the convolution algebra \({\mathcal D}\). If \(F^ N\cap \Delta_ c\neq \emptyset\), then the completion of C with respect to F- convergence is isomorphic to \(B_ F(C,\Delta_ c)\).
Mathematics Subject Classification ID: 44A40
Mathematics Subject Classification ID: 46F05
zbMATH DE Number: 4063769
zbMATH Keywords: regular operators
zbMATH Keywords: convergence
zbMATH Keywords: Boehmians
zbMATH Keywords: generalized functions
zbMATH Keywords: distributions
zbMATH Keywords: convolution algebra
author: Piotr Mikusiński
reviewed by: B. Stanković
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01903334
OpenAlex ID: W2063521300
description: scientific article; zbMATH DE number 4063769