An extremal problem for Dirichlet-finite holomorphic functions on Riemann surfaces (Q1065200)
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scientific article; zbMATH DE number 3920910
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An extremal problem for Dirichlet-finite holomorphic functions on Riemann surfaces |
scientific article; zbMATH DE number 3920910 |
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An extremal problem for Dirichlet-finite holomorphic functions on Riemann surfaces (English)
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1985
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Let R be a Riemann surface, f a nonconstant holomorphic function on R with finite Dirichlet integral D(f), and \(f_ 2\) the least harmonic majorant of f. Theorem: \(\pi\) \(\sum f_ 2(a)\leq D(f)\), the sum over all a for which \(f(a)=0\). Conditions for equality are given.
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Dirichlet integral
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