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Sampling in de Branges Spaces and Naimark Dilation

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Abstract

We consider the problem of sampling in de Branges spaces and develop some necessary conditions and some sufficient conditions for sampling sequences, which generalize some well-known sampling results in the Paley–Wiener space. These conditions are obtained by identifying the main construction with Naimark dilation of frames-embedding the de Branges space into a larger de Branges space while embedding the kernel functions associated with a sampling sequence into a Riesz basis for the larger space.

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Acknowledgments

We thank the anonymous referee for numerous helpful suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Hashemite University, Zarqa, Jordan

    Sa’ud al-Sa’di

  2. Department of Mathematics, Iowa State University, 396 Carver Hall, Ames, IA, 50011, USA

    Eric S. Weber

Authors
  1. Sa’ud al-Sa’di
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  2. Eric S. Weber
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Correspondence to Eric S. Weber.

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Communicated by Daniel Aron Alpay.

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al-Sa’di, S., Weber, E.S. Sampling in de Branges Spaces and Naimark Dilation. Complex Anal. Oper. Theory 11, 583–601 (2017). https://doi.org/10.1007/s11785-016-0580-1

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  • DOI: https://doi.org/10.1007/s11785-016-0580-1

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