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The Mystery of Gabor Frames

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This is a survey about the theory of Gabor frames. We review the structural results about Gabor frames over a lattice and then discuss the few known results about the fine structure of Gabor frames. We add a new result about the relation between properties of the window and properties of the frame set and conclude with a vision of how a more complete theory of the fine structure might look like.

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Acknowledgments

This survey owes a lot to inspiring and fruitful collaborations with Yura Lyubarski and Joachim Stöckler and to many exciting discussions with them. I would like to thank Christopher Heil for his invaluable advice on mathematical writing and Hans Feichtinger for his comments on the manuscript.

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  1. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 , Vienna, Austria

    Karlheinz Gröchenig

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  1. Karlheinz Gröchenig
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Correspondence to Karlheinz Gröchenig.

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Communicated by A.J.E.M. Janssen.

K. G. was supported in part by the projects P22746-N13 and P26273-N25 of the Austrian Science Fund (FWF) and by National Research Network S106 SISE of FWF.

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Gröchenig, K. The Mystery of Gabor Frames. J Fourier Anal Appl 20, 865–895 (2014). https://doi.org/10.1007/s00041-014-9336-3

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