An Equivalence between the Limit Smoothness and the Rate of Convergence for a General Contraction Operator Family
Joint Authors
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-5, 5 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-11-02
Country of Publication
Egypt
No. of Pages
5
Main Subjects
Abstract EN
Let X be a topological space equipped with a complete positive σ-finite measure and T a subset of the reals with 0 as an accumulation point.
Let atx,y be a nonnegative measurable function on X×X which integrates to 1 in each variable.
For a function f∈L2X and t∈T, define Atfx≡∫ atx,yfy dy.
We assume that Atf converges to f in L2, as t⟶0 in T.
For example, At is a diffusion semigroup (with T=0,∞).
For W a finite measure space and w∈W, select real-valued hw∈L2X, defined everywhere, with hwL2X≤1.
Define the distance D by Dx,y≡hwx−hwyL2W.
Our main result is an equivalence between the smoothness of an L2X function f (as measured by an L2-Lipschitz condition involving at·,· and the distance D) and the rate of convergence of Atf to f.
American Psychological Association (APA)
Goldberg, Maxim J.& Kim, Seonja. 2020. An Equivalence between the Limit Smoothness and the Rate of Convergence for a General Contraction Operator Family. Abstract and Applied Analysis،Vol. 2020, no. 2020, pp.1-5.
https://search.emarefa.net/detail/BIM-1119978
Modern Language Association (MLA)
Goldberg, Maxim J.& Kim, Seonja. An Equivalence between the Limit Smoothness and the Rate of Convergence for a General Contraction Operator Family. Abstract and Applied Analysis No. 2020 (2020), pp.1-5.
https://search.emarefa.net/detail/BIM-1119978
American Medical Association (AMA)
Goldberg, Maxim J.& Kim, Seonja. An Equivalence between the Limit Smoothness and the Rate of Convergence for a General Contraction Operator Family. Abstract and Applied Analysis. 2020. Vol. 2020, no. 2020, pp.1-5.
https://search.emarefa.net/detail/BIM-1119978
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1119978