## 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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