Operator semi-selfdecomposable measures and related nested subclasses of measures on vector spaces

Abstract

$T$-semi-selfdecomposability and subclasses $L_m(b,Q)$ and ${\tilde{L}}_m(b,Q)$ of measures on complete separable metric vector spaces are introduced and basic properties are proved. In particular, we show that $\mu$ is $T$-semi-selfdecomposable if and only if $\mu =T(\mu )\nu$ where $\nu$ is infinitely divisible and $\mu$ is operator selfdecomposable if and only if $\mu \in L_0(b,Q)$ for all $0<b<1$.

15 pages, revised version and Theorem 5 is modified