The heat kernel of the symmetric space \(\mathcal P_n\) (Q2716375)
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scientific article; zbMATH DE number 1598740
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The heat kernel of the symmetric space \(\mathcal P_n\) |
scientific article; zbMATH DE number 1598740 |
Statements
15 May 2001
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Laplace-Beltrami operator
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\(GL(n)\)
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heat equation
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heat kernel
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fundamental solution
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Hermite matrix
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The heat kernel of the symmetric space \(\mathcal P_n\) (English)
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Let \({\mathcal P}_n\) be the set of all \(n\times n\) Hermite positive defined matrices. \({\mathcal P}_n\) is considered as a homogeneous space for the group \(GL(n)\) of nonsingular \(n\times n\) complex matrices and let \(\Delta\) be the Laplace-Beltrami operator associated with the invariant Riemann metric on \({\mathcal P}_n\). The author computes the heat kernel (that is, the fundamental solution to the heat equation \((\Delta-\partial_t)f=0\)) on \({\mathcal P}_n\).
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