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Revista Matemática Complutense

, Volume 32, Issue 1, pp 115–139 | Cite as

Interpolating sequences for weighted spaces of analytic functions on the unit ball of a Hilbert space

  • Oscar Blasco
  • Pablo Galindo
  • Mikael Lindström
  • Alejandro MirallesEmail author
Article
  • 103 Downloads

Abstract

We show that an interpolating sequence for the weighted Banach space of analytic functions on the unit ball of a Hilbert space is hyperbolically separated. In the case of the so-called standard weights, a sufficient condition for a sequence to be linear interpolating is given in terms of Carleson type measures. Other conditions to be linearly interpolating are provided as well. Our results apply to the space of Bloch functions of such unit ball.

Keywords

Interpolating sequence Hyperbolically separated Bloch function in the ball Infinite dimensional holomorphy Weighted space of analytic functions 

Mathematics Subject Classification

Primary 30D45 46E50 Secondary 46G20 

Notes

Acknowledgements

This paper was completed during the 2016 fall semester while Mikael Lindström was visiting Universidad de Valencia whose hospitality is gratefully acknowledged with special thanks to Pablo Galindo. We warmly thank the referees for their very careful reading and the suggestions provided.

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Copyright information

© Universidad Complutense de Madrid 2018

Authors and Affiliations

  1. 1.Departamento de Análisis MatemáticoUniversidad de ValenciaValenciaSpain
  2. 2.Department of MathematicsAbo Akademi UniversityAboFinland
  3. 3.Departament de Matemàtiques and Instituto Universitario de Matemáticas y Aplicaciones de Castellón (IMAC)Universitat Jaume I de Castelló (UJI)CastellóSpain

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