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Frames on Locally Compact Abelian Groups

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An Introduction to Frames and Riesz Bases

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

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Abstract

In this chapter we will consider frame theory from a broader viewpoint than before, namely, as a part of general harmonic analysis. A central part of harmonic analysis deals with functions on groups and ways to decompose such functions in terms of either series representations or integral representations of certain “basic functions.” One of the strengths of harmonic analysis is that it allows very general results that cover several cases at once; for example, instead of developing parallel theories for various groups, we might obtain all of them as special manifestations of a single theory.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark

    Ole Christensen

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  1. Ole Christensen
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Christensen, O. (2016). Frames on Locally Compact Abelian Groups. In: An Introduction to Frames and Riesz Bases. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-25613-9_21

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