TY - GEN

T1 - Random Tempered Distributions on Locally Compact Separable Abelian Groups

AU - Esquível, Manuel L.

AU - Krasii, Nadezhda P.

N1 - Funding Information:
Centro de Matemática e Aplicações, UID/MAT/00297/2020
Russian Foundation for Basic Research (RFBR) (grant no. 19-01-00451).
Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Analysis on separable locally compact abelian groups

KW - Cantor group

KW - Generalised functions on infinite-dimensional spaces

KW - Generalised stochastic processes

UR - http://www.scopus.com/inward/record.url?scp=85115248679&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-76829-4_7

DO - 10.1007/978-3-030-76829-4_7

M3 - Conference contribution

AN - SCOPUS:85115248679

SN - 9783030768287

T3 - Springer Proceedings in Mathematics and Statistics

SP - 147

EP - 166

BT - Operator Theory and Harmonic Analysis, OTHA 2020

A2 - Karapetyants, Alexey N.

A2 - Pavlov, Igor V.

A2 - Shiryaev, Albert N.

PB - Springer

T2 - International Scientific Conference on Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis, OTHA 2020

Y2 - 26 April 2020 through 30 April 2020

ER -