Interpolation on plane sets in \({\mathbb{C}}^ 2\) (Q1261241)
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scientific article; zbMATH DE number 404400
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Interpolation on plane sets in \({\mathbb{C}}^ 2\) |
scientific article; zbMATH DE number 404400 |
Statements
Interpolation on plane sets in \({\mathbb{C}}^ 2\) (English)
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31 August 1993
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The authors investigate analytic and geometric conditions which ensure that holomorphic functions defined on analytic varieties in \(\mathbb{C}^ 2\) can be extended analytically to all of \(\mathbb{C}^ 2\), satisfying certain growth estimates. The analytic varieties considered are unions of countable families of hyperplanes. The results obtained generalize work of A. F. Grishin and the second author [\textit{A. F. Grishin}, Teor. Funkts., Funkts. Anal. Prilozh. 40, 36-47 (1983; Zbl 0601.40036) and \textit{A. F. Grishin} and the second author, J. Sov. Math. 48, No. 3, 267-275 (1990); translation from Teor. Funkts., Funkts. Anal. Prilozh. 44, 32-42 (1985; Zbl 0577.30031)], in which interpolatory divisors in \(\mathbb{C}\) are characterized analytically and geometrically.
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holomorphic functions
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analytic varieties
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growth estimates
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interpolatory divisors
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