Real analytic version of Lévy's theorem (Q2825912)
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scientific article; zbMATH DE number 6638664
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Real analytic version of Lévy's theorem |
scientific article; zbMATH DE number 6638664 |
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13 October 2016
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absolutely convergent Fourier series
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commutative Banach algebra
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functional calculus
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weighted algebra
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real analytic function
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Real analytic version of Lévy's theorem (English)
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The classical result of Paul Lévy says that holomorphic functions act on the algebra of absolutely convergent Fourier series. More precisely: if \(f\) is a function having an absolutely convergent Fourier series, \(f(t)= \Sigma_{n\in \mathbb{Z}}a_ne^{\imath nt}\), then, for any function \(F\) that is holomorphic in a domain containing the range of \(f\), the composition \(F\circ f\) also has an absolutely convergent Fourier series. The paper under review gives a weighted version of this result for the action of analytic functions of two real variables.
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0.7921562194824219
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0.7766484618186951
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