The Young type theorem in weighted Fock spaces

Anton Baranov, Yurii Belov, Alexander Borichev

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We prove that for every radial weighted Fock space, the system biorthogonal to a complete and minimal system of reproducing kernels is also complete under very mild regularity assumptions on the weight. This result generalizes a theorem by Young on reproducing kernels in the Paley–Wiener space and a recent result of Belov for the classical Bargmann–Segal–Fock space.

Original languageEnglish
Pages (from-to)357-363
Number of pages7
JournalBulletin of the London Mathematical Society
Volume50
Issue number2
DOIs
StatePublished - 1 Apr 2018

Keywords

  • 30B60 (primary)
  • 30D10
  • 30D15
  • 30H20
  • 42A63 (secondary)

Scopus subject areas

  • Mathematics(all)

Cite this

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The Young type theorem in weighted Fock spaces. / Baranov, Anton; Belov, Yurii; Borichev, Alexander.

In: Bulletin of the London Mathematical Society, Vol. 50, No. 2, 01.04.2018, p. 357-363.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Belov, Yurii

AU - Borichev, Alexander

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N2 - We prove that for every radial weighted Fock space, the system biorthogonal to a complete and minimal system of reproducing kernels is also complete under very mild regularity assumptions on the weight. This result generalizes a theorem by Young on reproducing kernels in the Paley–Wiener space and a recent result of Belov for the classical Bargmann–Segal–Fock space.

AB - We prove that for every radial weighted Fock space, the system biorthogonal to a complete and minimal system of reproducing kernels is also complete under very mild regularity assumptions on the weight. This result generalizes a theorem by Young on reproducing kernels in the Paley–Wiener space and a recent result of Belov for the classical Bargmann–Segal–Fock space.

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