Action of Ornstein-Uhlenbeck Semigroup on (w1,w2)-Tempered Ultradistributions

Authors

Maysam Abu-Dalu, Department of Mathematics, Hashemite University, P.O.Box 150459, Zarqa 13115, JordanFollow
Ala Qadomi, Department of Mathematics, Hashemite University, P.O.Box 150459, Zarqa 13115, JordanFollow
Sa’ud Al-Sa’di, Department of Mathematics, Hashemite University, P.O.Box 150459, Zarqa 13115, JordanFollow

Author Country (or Countries)

Jordan

Abstract

Using a previously obtained structure theorem for (w1,w2)-tempered ultradistributions by the classical Riesz representation theorem, we investigate the action of the Ornstein-Uhlenbeck semigroup on (w1,w2)-tempered ultradistributions. As a result, we observe that these tempered ultradistributions can be represented as boundary values to the heat equation ut − Au = 0, for t > 0.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/140310

Recommended Citation

Abu-Dalu, Maysam; Qadomi, Ala; and Al-Sa’di, Sa’ud (2020) "Action of Ornstein-Uhlenbeck Semigroup on (w1,w2)-Tempered Ultradistributions," Applied Mathematics & Information Sciences: Vol. 14: Iss. 3, Article 10.
DOI: http://dx.doi.org/10.18576/amis/140310
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss3/10