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On Density Conditions for Interpolation in the Ball

Published online by Cambridge University Press:  20 November 2018

Nicolas Marco  and
Xavier Massaneda
Nicolas Marco
Affiliation:
Departament de Matemàtiques Universitat Autònoma de Barcelona 08193 Bellaterra Spain, e-mail: [email protected]
Xavier Massaneda
Affiliation:
Departament de Matemàtica Aplicada i Anàlisi Universitat de Barcelona Gran Via 585 08071 Barcelona Spain, e-mail: [email protected]
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Abstract

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In this paper we study interpolating sequences for two related spaces of holomorphic functions in the unit ball of ${{\mathbb{C}}^{n}},\,n\,>\,1$. We first give density conditions for a sequence to be interpolating for the class ${{A}^{-\infty }}$ of holomorphic functions with polynomial growth. The sufficient condition is formally identical to the characterizing condition in dimension 1, whereas the necessary one goes along the lines of the results given by Li and Taylor for some spaces of entire functions. In the second part of the paper we show that a density condition, which for $n\,=\,1$ coincides with the characterizing condition given by Seip, is sufficient for interpolation in the (weighted) Bergman space.

Keywords

32A3632A3830E05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 4 , 01 December 2003 , pp. 559 - 574
Copyright
Copyright © Canadian Mathematical Society 2003

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