Elliptic differential operators on Lie groups (Q1175013)
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scientific article; zbMATH DE number 9901
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Elliptic differential operators on Lie groups |
scientific article; zbMATH DE number 9901 |
Statements
Elliptic differential operators on Lie groups (English)
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25 June 1992
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Strongly elliptic operators in the enveloping Lie algebra associated with a continuous representation of a Lie group are considered. Boundedness and analyticity properties of holomorphic semigroups generated by such operators and their kernels K are studied. Particularly, pointwise bounds and \(L_ p \) bounds on K and its higher derivatives are given. No symmetry assumptions are considered. For this investigation, a new version of the Nash inequality for the differential structure of the group representation is derived. As an application, Sobolev embedding theorems for Lie groups are given.
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strongly elliptic operators
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enveloping Lie algebra
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continuous representation of a Lie group
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boundedness
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analyticity
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holomorphic semigroups
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pointwise bounds
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\(L_ p\) bounds
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no symmetry assumptions
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Nash inequality
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differential structure of the group representation
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Sobolev embedding theorems for Lie groups
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