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Interpolation and sampling hypersurfaces for the Bargmann-Fock space in higher dimensions

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Abstract

We study those smooth complex hypersurfaces W in having the property that all holomorphic functions of finite weighted L p norm on W extend to entire functions with finite weighted L p norm. Such hypersurfaces are called interpolation hypersurfaces. We also examine the dual problem of finding all sampling hypersurfaces, i.e., smooth hypersurfaces W in such that any entire function with finite weighted L p norm is stably determined by its restriction to W.

We provide sufficient geometric conditions on the hypersurface to be an interpolation or sampling hypersurface. The geometric conditions that imply the extension property and the restriction property are given in terms of some directional densities.

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Authors and Affiliations

  1. Departament de Matemàtica Applicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08071, Barcelona, Spain

    Joaquim Ortega-Cerdà

  2. Department of Mathematics, San Francisco State University, San Francisco, CA, 94132

    Alexander Schuster

  3. Department of Mathematics, Stony Brook University, Stony Brook, NY, 11794

    Dror Varolin

Authors
  1. Joaquim Ortega-Cerdà
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  2. Alexander Schuster
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  3. Dror Varolin
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Corresponding author

Correspondence to Dror Varolin.

Additional information

The first author is supported by projects MTM 2005-08984-Co2-O2 and 2001SGR00611

The third author is partially supported by NSF grant DMS0400909

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Ortega-Cerdà, J., Schuster, A. & Varolin, D. Interpolation and sampling hypersurfaces for the Bargmann-Fock space in higher dimensions. Math. Ann. 335, 79–107 (2006). https://doi.org/10.1007/s00208-005-0726-3

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  • DOI: https://doi.org/10.1007/s00208-005-0726-3

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