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Wavelets and Multiscale Analysis pp 131–150Cite as

Unitary Systems and Bessel Generator Multipliers

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

Abstract

A Bessel generator multiplier for a unitary system is a bounded linear operator that sends Bessel generator vectors to Bessel generator vectors. We characterize some special (but useful) Bessel generator multipliers for the unitary systems that are ordered products of two unitary groups. These include the wavelet and the Gabor unitary systems. We also provide a detailed exposition of some of the history leading up to this work.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, College Station, TX, USA

    David R. Larson

Authors
  1. Deguang Han
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  2. David R. Larson
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Correspondence to David R. Larson .

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Editors and Affiliations

  1. , Department of Mathematical Sciences, DePaul University, North Kenmore Avenue 2320, Chicago, 60614-3250, Illinois, USA

    Jonathan Cohen

  2. , Department of Mathematical Sciences, DePaul University, North Kenmore Avenue 2320, Chicago, 60614-3250, Illinois, USA

    Ahmed I. Zayed

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Han, D., Larson, D.R. (2011). Unitary Systems and Bessel Generator Multipliers. In: Cohen, J., Zayed, A. (eds) Wavelets and Multiscale Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8095-4_7

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