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Russian Mathematics

, Volume 63, Issue 2, pp 51–61 | Cite as

Existence of Frames Based on the Szegö Kernel in the Hardy Space

  • K. S. SperanskyEmail author
  • P. A. TerekhinEmail author
Article
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Abstract

As is known, a sequence of functions consisting of meanings of the Szegö reproducing kernel of the Hardy space in the unit disk cannot be Duffin—Schaeffer frame. In the present paper we show that the using of more general conception of frame enables us to solve positively the question on existence of a generalized frame built in terms of the Szegö kernel.

Key words

Duffin—Schaeffer frame Banach frame model space of frame reproducing kernel of Hilbert space Hardy space Szegö kernel 

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Notes

Acknowledgments

The research is performed with support of Russian Foundation for Basic Researches (grant No. 18-01-00414).

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© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Saratov State UniversitySaratovRussia

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