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 -