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Bounded analytic structure of the Banach space of formal power series. (English) Zbl 1194.47035

Summary: Let \(\{ \beta (n)\} _{n = 0}^\infty \) be a sequence of positive numbers and \(1\leq p< \infty\). We consider the space \(H^p(\beta)\) of all power series \(f(z) = \sum_{n = 0}^\infty \hat{f}(n)z^n \) such that \(\sum |\hat{f}(n)|^p \beta (n)^p< \infty \). We investigate regions on which our formal power series represent bounded analytic functions.

MSC:

47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47A25 Spectral sets of linear operators
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References:

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