An identity theorem for logarithmic potentials (Q1197474)
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scientific article; zbMATH DE number 91626
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An identity theorem for logarithmic potentials |
scientific article; zbMATH DE number 91626 |
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An identity theorem for logarithmic potentials (English)
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16 January 1993
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The main result of the paper is the uniqueness theorem for superharmonic functions on the complex plane. Conditions of uniqueness are formulated in terms of their growth and their behaviour on a subset of the union of Riesz measures' supports, provided that this subset has finitely many connected components and its closure is the union of these supports. This theorem gives an answer to a question put by \textit{R. Grothmann} [Can. J. Math. 40, No. 2, 477-486 (1988; Zbl 0661.31007)]\ concerning a uniqueness criterion for representing measures of logarithmic potentials.
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Green function
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logarithmic potential
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thinness at a point
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uniqueness theorem for superharmonic functions
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complex plane
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representing measures
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