Journal of Fourier Analysis and Applications

, Volume 20, Issue 4, pp 865–895 | Cite as

The Mystery of Gabor Frames

Article
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Abstract

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.

Keywords

Gabor frame Time–frequency shift Lattice 
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Notes

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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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria

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