On a Gaussian free measure on the space of distributions over the field of \(p\)-adic numbers. (Q2754849)
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scientific article; zbMATH DE number 1668468
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a Gaussian free measure on the space of distributions over the field of \(p\)-adic numbers. |
scientific article; zbMATH DE number 1668468 |
Statements
4 November 2001
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Gaussian measure
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Schwartz-Bruhat space
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Green function
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elliptic pseudo-differential operator
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On a Gaussian free measure on the space of distributions over the field of \(p\)-adic numbers. (English)
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The author considers a Gaussian free measure \(\mu\) on the Schwartz-Bruhat space \(\mathcal D'(\mathbb Q_p^d)\) corresponding to the Green function of the elliptic pseudo-differential operator with the symbol \(| h(\xi_1,\ldots ,\xi_d)|_p^\alpha\), \(\alpha >0\), where \(h\) is an anisotropic quadratic form over \(\mathbb Q_p\), \(d\leq 4\). Sets of full measure for \(\mu\) are found.
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