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Sparse exponential systems: Completeness with estimates

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Abstract

According to A. Beurling and H. Landau, if an exponential system {e iλt}λ∈Λ is a frame in L 2 on a set S of positive measure, then Λ must satisfy a strong density condition. We replace the frame concept by a weaker condition and prove that if S is a finite union of segments then the result holds. However, for “generic” S, very sparse sequences Λ are admitted.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv, 69978, Israel

    Shahaf Nitzan-Hahamov & Alexander Olevskii

Authors
  1. Shahaf Nitzan-Hahamov
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  2. Alexander Olevskii
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Supported in part by the Israel Science Foundation.

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Nitzan-Hahamov, S., Olevskii, A. Sparse exponential systems: Completeness with estimates. Isr. J. Math. 158, 205–215 (2007). https://doi.org/10.1007/s11856-007-0010-1

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  • DOI: https://doi.org/10.1007/s11856-007-0010-1

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