Borel transforms of functions from a parameterized family of Hilbert spaces of entire functions

Konstantin Isaev; Rinad Yulmukhametov

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arXiv · 2404.11548

Borel transforms of functions from a parameterized family of Hilbert spaces of entire functions

Konstantin Isaev·Rinad Yulmukhametov

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Abstract

We introduce a continuous scale of Hilbert spaces of entire functions $P_β(D)$ for a bounded convex domain $D$ on the complex plane. For the parameters $β\in (\frac 12;\frac 32)$ a complete description of the spaces of Borel transforms of functions from $P_β(D)$ is given.

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BibTeX RIS

Konstantin Isaev, Rinad Yulmukhametov. 2024-04-17. Borel transforms of functions from a parameterized family of Hilbert spaces of entire functions. https://arxiv.org/abs/2404.11548

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