๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Analyticity and Injectivity of Convolution Semigroups on Lie Groups

โœ Scribed by Hiroshi Kunita

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
165 KB
Volume
165
Category
Article
ISSN
0022-1236

No coin nor oath required. For personal study only.

โœฆ Synopsis

We prove that all continuous convolution semigroups of probability distributions on an arbitrary Lie group are injective. Let [+ t , t>0] be a continuous convolution semigroup of probability distributions on a Lie group G. For each t>0, we set T t f (x)= G f (xy) + t (dy) for a bounded continuous function f. We show that T t f =0 holds if and only if f =0. This fact will be applied in proving the unique divisibleness of the convolution product for a certain distribution. We show that & V !=& V !$ implies !=!$, provided that & is an infinitely divisible distribution on a simply connected nilpotent Lie group.

๐Ÿ“œ SIMILAR VOLUMES

Asymmetry of Convolution Norms on Lie Gr
Asymmetry of Convolution Norms on Lie Groups
โœ A.H. Dooley; Sanjiv Kumar Gupta; Fulvio Ricci ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 151 KB

We prove that on most connected non-commutative Lie groups there exists a convolution operator which is bounded on L p but unbounded on L q for every q not belonging to the interval with endpoints 2 and p. Furthermore, the kernel of such an operator can be supported on an arbitrary neighbourhood of

Analysis of a Distinguished Laplacian on
Analysis of a Distinguished Laplacian on Solvable Lie Groups
โœ Saverio Giulini; Giancarlo Mauceri ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 575 KB

## Abstract We study a class of kernels associated to functions of a distinguished Laplacian on the solvable group __AN__ occurring in the Iwasawa decomposition __G__ = __ANK__ of a noncompact semisimple Lie group __G.__ We determine the maximal ideal space of a commutative subalgebra of __L__^1^,