Operators commuting with the multiple integration in the space of analytic functions (Q1084644)
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scientific article; zbMATH DE number 3979835
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Operators commuting with the multiple integration in the space of analytic functions |
scientific article; zbMATH DE number 3979835 |
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Operators commuting with the multiple integration in the space of analytic functions (English)
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1986
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Let D be a star-shaped (w.r.t. zero) domain in the complex plane. Let \((If)(z)=\int^{z}_{0}f(\zeta)d\zeta\) be the integration operator in the space A(D) of analytic functions on D. Let p be a positive integer. The author describes the commutant of \(I^ p\) in A(D). The results depend on the rotation properties of D. Similar results are obtained for the multiplication operator \((Uf)(z)=zf(z)\).
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operator in the space of analytic functions
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commutant
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rotation
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multiplication operator
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