Martin representation for \(\alpha\)-harmonic functions (Q2772040)
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scientific article; zbMATH DE number 1706583
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Martin representation for \(\alpha\)-harmonic functions |
scientific article; zbMATH DE number 1706583 |
Statements
18 February 2002
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\(\alpha\)-harmonic function
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Martin kernel
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Martin representation
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Martin representation for \(\alpha\)-harmonic functions (English)
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Let \(D\) be a nonempty open bounded subset of \({\mathbf R}^d\), \(d\geq 2\), and let \(0<\alpha<2\). The authors prove a Martin integral representation of \(\alpha\)-harmonic functions on \(D\) vanishing outside \(D\). Mixing analytic and probabilistic techniques, the authors adapt, in a nontrivial way, the classical Martin proof for harmonic functions.
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