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Mediterranean Journal of Mathematics

, Volume 11, Issue 2, pp 643–652 | Cite as

The Range of the Restriction Map for a Multiplicity Variety in Hörmander Algebras of Entire Functions

  • José Bonet
  • Carmen Fernández
Article

Abstract

Characterizations of interpolating multiplicity varieties for Hörmander algebras \({A_p(\mathbb{C})}\) and \({A^0_p(\mathbb{C})}\) of entire functions were obtained by Berenstein and Li (J Geom Anal 5(1):1–48, 1995) and Berenstein et al. (Can J Math 47(1):28–43, 1995) for a radial subharmonic weight p with the doubling property. In this note we consider the case when the multiplicity variety is not interpolating, we compare the range of the associated restriction map for two weights \({q \leq p}\) and investigate when the range of the restriction map on \({A_p(\mathbb{C})}\) or \({A^0_p(\mathbb{C})}\) contains certain subspaces associated in a natural way with the smaller weight q.

Mathematics Subject Classification (2010)

Primary 46E10 Secondary 30D15 30D20 30E05 46A04 

Keywords

Discrete interpolating varieties entire functions growth conditions weighted spaces of entire functions 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Instituto Universitario de Matemática Pura y Aplicada IUMPAUniversitat Politècnica de ValènciaValenciaSpain
  2. 2.Departamento de Análisis MatemáticoUniversidad de ValenciaBurjassotSpain

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