Inversions of Hermite semigroup

Byun, Du-Won

doi:10.1090/S0002-9939-1993-1145414-6

Inversions of Hermite semigroup
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Proc. Amer. Math. Soc. 118 (1993), 437-445 Request permission

Abstract:

Let $\{ {e^{ - cH}}|c \geqslant 0\}$ be the Hermite semigroup on the real line $\mathbb {R}$. Then a representation is constructed for inversions of the semigroup, and it gives a representation of ${e^{ - cH}}$ for $c < 0$. Moreover, some characterizations of the domain in which, for $c < 0,\;{e^{ - cH}}$ is well defined are examined.

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