Operator Semi-Selfdecomposable Measures and Related Nested Subclasses of Measures on Vector Spaces

摘要

T-semi-selfdecomposability, operator selfdecomposability, and subclasses L m (b, (T t )) and ${tilde L}_m (b, (T_t))$ of measures on complete separable metric vector spaces are introduced and basic properties are proved. In particular, we show that μ is T-semi-selfdecomposable if and only if μ = T(μ) ν where ν is infinitely divisible and μ is operator selfdecomposable if and only if μ∈L 0(b, (T t )) for all 0 < b < .