Random Tempered Distributions on Locally Compact Separable Abelian Groups

Manuel L. Esquível, Nadezhda P. Krasii

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

By means of sequences of random variables of controlled growth, that is, either rapidly decreasing or slowly increasing, we define a space of random tempered generalized functions—of Schwartz type—on a locally compact abelian separable group, and we characterize the set of those generalized functions that have a mean. We show that this approach covers both the case of the torus and the real line case and also allows us to define tempered random distributions over the Cantor set by means of the associated Cantor group.

Original languageEnglish
Title of host publicationOperator Theory and Harmonic Analysis, OTHA 2020
EditorsAlexey N. Karapetyants, Igor V. Pavlov, Albert N. Shiryaev
PublisherSpringer
Pages147-166
Number of pages20
ISBN (Print)9783030768287
DOIs
Publication statusPublished - 2021
EventInternational Scientific Conference on Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis, OTHA 2020 - Rostov-on-Don, Russian Federation
Duration: 26 Apr 202030 Apr 2020

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume358
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational Scientific Conference on Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis, OTHA 2020
Country/TerritoryRussian Federation
CityRostov-on-Don
Period26/04/2030/04/20

Keywords

  • Analysis on separable locally compact abelian groups
  • Cantor group
  • Generalised functions on infinite-dimensional spaces
  • Generalised stochastic processes

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