Frames of translates for number-theoretic groups

John J. Benedetto; Robert L. Benedetto

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arXiv · 1804.07783

Frames of translates for number-theoretic groups

John J. Benedetto·Robert L. Benedetto

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Abstract

Frames of translates of f in L^2(G) are characterized in terms of the zero-set of the so-called spectral symbol of f in the setting of a locally compact abelian group G having a compact open subgroup H. We refer to such a G as a number theoretic group. This characterization was first proved in 1992 by Shidong Li and one of the authors for L^2(R^d) with the same formal statement of the characterization. For number theoretic groups, and these include local fields, the strategy of proof is necessarily entirely different; and it requires a new notion of translation that reduces to the usual definition in R^d.

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John J. Benedetto, Robert L. Benedetto. 2018-04-20. Frames of translates for number-theoretic groups. https://arxiv.org/abs/1804.07783

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