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

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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.

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Authors and Affiliations

  1. Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universitat Politècnica de València, 46071, Valencia, Spain

    José Bonet

  2. Departamento de Análisis Matemático, Universidad de Valencia, 46100, Burjassot, Spain

    Carmen Fernández

Authors
  1. José Bonet
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  2. Carmen Fernández
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Correspondence to José Bonet.

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Bonet, J., Fernández, C. The Range of the Restriction Map for a Multiplicity Variety in Hörmander Algebras of Entire Functions. Mediterr. J. Math. 11, 643–652 (2014). https://doi.org/10.1007/s00009-013-0318-5

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  • DOI: https://doi.org/10.1007/s00009-013-0318-5

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