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arXiv · 1601.08144

Monomial convergence for holomorphic functions on $\ell\_r$

Frédéric Bayart·Andreas Defant·Sunke Schlüters
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Abstract

Let $\mathcal F$ be either the set of all bounded holomorphic functions or the set of all $m$-homogeneous polynomials on the unit ball of $\ell\_r$. We give a systematic study of the sets of all $u\in\ell\_r$ for which the monomial expansion $\sum\_α\frac{\partial^αf(0)}{α!}u^α$ of every $f\in\mathcal F$ converges. Inspired by recent results from the general theory of Dirichlet series, we establish as our main tool, independently interesting, upper estimates for the unconditional basis constants of spaces of polynomials on $\ell\_r$ spanned by finite sets of monomials.

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BibTeXRIS

Frédéric Bayart, Andreas Defant, Sunke Schlüters. 2016-01-29. Monomial convergence for holomorphic functions on $\ell\_r$. https://arxiv.org/abs/1601.08144

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