The nonexistence of regularization operators.
type: Item
instance of: scholarly article
title: The nonexistence of regularization operators.
zbMATH Open document ID: 1038.46028
DOI: 10.1016/S0022-247X(02)00424-9
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-11-16T00:00:00Z
review text: With references to applications in physics the author discusses the well known problem of regularization of generalized functions. As is known, there exist various procedures to regularize some concrete classes of generalized functions. For generalized functions on the real line the author shows that there cannot exist a unique procedure which provides continuous regularization of all the generalized function (under a certain definition of what regularization is). The author also develops these ideas to prove the nonexistence of continuous restrictions into spaces of distributions defined on a closed set. The latter, as the author observes, is important in the study of integral equations in spaces of generalized functions.
Mathematics Subject Classification ID: 46F05
zbMATH DE Number: 2003884
zbMATH Keywords: distributions
zbMATH Keywords: regularization
author: R. Estrada
reviewed by: S. G. Samko
MaRDI profile type: Publication
cites work: Q3261267
cites work: Regularization of distributions
cites work: How singular functions define distributions
cites work: Q3695796
cites work: Taylor expansions for distributions
cites work: A distributional approach to the boundary layer theory
cites work: Q5724171
cites work: Q5518756
cites work: Q5624183
cites work: Distributions and singular integral equations of carleman type
cites work: Q4858557
cites work: Q5528072
cites work: Q5557339
full work available at URL: s0022-247x(02)00424-9
OpenAlex ID: W2025338618
description: scientific article; zbMATH DE number 2003884