On semigroups generated by differential operators on Lie groups
✍ Scribed by Jan Kisyński
- Publisher
- Elsevier Science
- Year
- 1979
- Tongue
- English
- Weight
- 620 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0022-1236
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📜 SIMILAR VOLUMES
This paper is devoted to the study of contraction semigroups generated by linear partial differential operators. It is shown that linear partial differential operators of order higher than two cannot generate contraction semigroups on (L p ) N for p # [1, ) unless p=2. If p>1 and the L p -dissipativ
Let U be a continuous representation of a Lie group G on a Banach space X and a 1 , ..., a d $ an algebraic basis of the Lie algebra g of G, i.e., the a 1 , ..., a d $ together with their multi-commutators span g. Let A i =dU(a i ) denote the infinitesimal generator of the continuous one-parameter g
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 fu