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)
Abu-Dalu, Maysam; Qadomi, Ala; and Al-Sa’di, Sa’ud
"Action of Ornstein-Uhlenbeck Semigroup on (w1,w2)-Tempered Ultradistributions,"
Applied Mathematics & Information Sciences: Vol. 14
, Article 10.
Available at: https://dc.naturalspublishing.com/amis/vol14/iss3/10