Skip to main content
SpringerLink
Log in

On interpolating varieties for weighted spaces of entire functions

  • Published:
The Journal of Geometric Analysis Aims and scope Submit manuscript

Abstract

Berenstein and Li recently gave a very complete description (in analytic and in geometric terms) of the interpolating varieties for various weighted spaces of entire and meromorphic functions in the complex plane. In this paper we use L2-estimates for\(\bar \partial \) (as in recent work of Berndtsson and Ortega Cerdà) to give easier proofs of some related results. In particular, we recover the geometric characterization of interpolating varieties for the space of entire functions of order smaller or equal to ρ > 0. In the higher dimensional case, the same technique provides a sufficient condition for interpolation on discrete varieties. This condition is not necessary in general, and it complements the results of Ounaies and Li and Taylor on the subject.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bemdtsson, B. and Ortega-Cerdà, J. On interpolation and sampling in Hilbert spaces of analytic functions.J. reine angew. Math.,464, 109–128. (1995).

    MathSciNet  Google Scholar 

  2. Berenstein, C.A. and Gay, R.Complex Analysis and Special Topics in Harmonic Analysis, Springer-Verlag, Berlin, 1995.

    MATH  Google Scholar 

  3. Berenstein, C.A. and Li, B.Q. Interpolating varieties for spaces of meromorphic functions,J. Geom. Anal.,5, 1–48, (1995).

    Article  MathSciNet  MATH  Google Scholar 

  4. Hörmander, L.An Introduction to Complex Analysis in Several Variables, Van Nostrand, 1966.

  5. Li, B.Q. and Taylor, B.A. On the Bézout problem and area of interpolating varieties in ℂn,Am. J. Math.,118, 989–1010, (1996).

    Article  MathSciNet  MATH  Google Scholar 

  6. Massaneda, X. and Thomas, P.J. Interpolating sequences for Bargmann-Fock spaces in ℂn,Indag. Math., N.S.,11(1), 115–127, (1998).

    Article  MathSciNet  Google Scholar 

  7. Ortega-Cerdà, J. and Seip, K. Beurling-type density theorems for weightedL p spaces of entire functions,J. Anal. Math.,75, 247–266, (1998).

    Article  MathSciNet  MATH  Google Scholar 

  8. Ounaies, M. Interpolating discrete varieties for spaces of entire functions with growth conditions, preprint, 1998.

  9. Seip, K. Density theorems for sampling and interpolation in the Bargmann-Fock space I,J. reine angew. Math.,429, 91–106, (1992).

    MathSciNet  MATH  Google Scholar 

  10. Seip, K. and Wallstén, R. Density theorems for sampling and interpolation in the Bargmann-Fock space II,J. reine angew. Math.,429, 107–113, (1992).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Mathématiques Pures, UFR Mathématiques/Informatique, Université Bordeaux I, 351, cours de la Libération, 33405, Talence/Cedex

    Andreas Hartmann

  2. Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08071, Barcelona, Spain

    Xavier Massaneda

Authors
  1. Andreas Hartmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xavier Massaneda
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andreas Hartmann.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hartmann, A., Massaneda, X. On interpolating varieties for weighted spaces of entire functions. J Geom Anal 10, 683–696 (2000). https://doi.org/10.1007/BF02921992

Download citation

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02921992

Math Subject Classifications

Key Words and Phrases

Search

Navigation