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Sampling: Theory and Applications pp 169–192Cite as

Birkhäuser

A Survey on the Unconditional Convergence and the Invertibility of Frame Multipliers with Implementation

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

Abstract

The paper presents a survey over frame multipliers and related concepts. In particular, it includes a short motivation of why multipliers are of interest to consider, a review as well as extension of recent results, devoted to the unconditional convergence of multipliers, sufficient and/or necessary conditions for the invertibility of multipliers, and representation of the inverse via Neumann-like series and via multipliers with particular parameters. Multipliers for frames with specific structure, namely Gabor multipliers, are also considered. Some of the results for the representation of the inverse multiplier are implemented in Matlab-codes and the algorithms are described.

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Notes

  1. 1.

    http://ltfat.github.io/doc/base/mulaclab.html.

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Acknowledgements

The authors acknowledge support from the Austrian Science Fund (FWF) START—project FLAME (‘Frames and Linear Operators for Acoustical Modeling and Parameter Estimation’; Y 551-N13). They thank Z. Prusa for help with LTFAT.

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Authors and Affiliations

  1. Acoustics Research Institute, Vienna, Austria

    Diana T. Stoeva & Peter Balazs

Authors
  1. Diana T. Stoeva
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  2. Peter Balazs
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Corresponding author

Correspondence to Diana T. Stoeva .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, American University, Washington, DC, USA

    Stephen D. Casey

  2. Norbert Wiener Center, University of Maryland, College Park, MD, USA

    Kasso A. Okoudjou

  3. Department of Mathematics and Statistics, American University, Washington, DC, USA

    Michael Robinson

  4. Army Research Laboratory, Adelphi, MD, USA

    Brian M. Sadler

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Stoeva, D.T., Balazs, P. (2020). A Survey on the Unconditional Convergence and the Invertibility of Frame Multipliers with Implementation. In: Casey, S., Okoudjou, K., Robinson, M., Sadler, B. (eds) Sampling: Theory and Applications. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-36291-1_6

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