The heat semigroup and integrability of Lie algebras: Lipschitz spaces and smoothness properties (Q2639943)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The heat semigroup and integrability of Lie algebras: Lipschitz spaces and smoothness properties |
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The heat semigroup and integrability of Lie algebras: Lipschitz spaces and smoothness properties (English)
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1990
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The paper under review deals with the integrability of Lie algebra representations. The main result is a considerable improvement of the results given in J. Funct. Anal. 79, 351-397 (1988; Zbl 0662.22009). More precisely, one associates a heat semigroup S with a well behaved representation of a Lie algebra. The integrability of the representation can then be characterized by certain smoothness and boundedness conditions on S. The author analyses the action of S and related one- parameter semigroups on various function spaces of Lipschitz type and as a result obtains that much weaker smoothness and boundedness conditions suffice to guarantee integrability.
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Lipschitz space
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integrability of Lie algebra representations
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heat semigroup
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smoothness
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boundedness
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one-parameter semigroups
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