Sparse exponential systems: Completeness with estimates |
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Authors: | Shahaf Nitzan-Hahamov Alexander Olevskii |
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Institution: | (1) School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv, 69978, Israel |
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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.
Supported in part by the Israel Science Foundation. |
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Keywords: | |
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