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Monomial Convergence for Holomorphic Functions on $\Ell\_r$ by Bayart, Frédéric; Defant, Andreas; Schlüters, Sunke is a scholarly article available to read on EtoBox.

What is Monomial Convergence for Holomorphic Functions on $\Ell\_r$ about?

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 $\sum\_{\alpha}\frac{\partial^\alpha f(0)}{\alpha !}u^\alpha$ 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.

Author

Bayart, Frédéric; Defant, Andreas; Schlüters, Sunke

Published

2016

Language

EN