Generalized spherical distributions on the Heisenberg group (Q2764829)
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scientific article; zbMATH DE number 1691030
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Generalized spherical distributions on the Heisenberg group |
scientific article; zbMATH DE number 1691030 |
Statements
27 February 2002
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spherical distribution
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unitary representation
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spherical Fourier transformation
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Generalized spherical distributions on the Heisenberg group (English)
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In this paper, a spherical distribution on a homogeneous space \(X=G/K\), where \(G\) is a unimodular Lie group and \(K\) a fixed compact subgroup in \(G\), is a distribution which is \(K\)-invariant and which is an eigendistribution for invariant differential operators on \(X\). This is a generalization of the same notion formulated by Takahashi in the case when \(K\) is a maximal compact subgroup in \(G\). The authors study the case of the Heisenberg group: In Theorem 2, the spherical Fourier transformation is described.
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