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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Department of Applied Mathematics and Computer Science, Technical University of Denmark, Building 303, Lyngby,2800, DenmarkDepartment of Applied Mathematics and Computer Science, Technical University of Denmark, Building 303, Lyngby,2800, Denmark
Christensen, Ole
Hasannasab, Marzieh
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Department of Applied Mathematics and Computer Science, Technical University of Denmark, Building 303, Lyngby,2800, DenmarkDepartment of Applied Mathematics and Computer Science, Technical University of Denmark, Building 303, Lyngby,2800, Denmark
Hasannasab, Marzieh
Philipp, Friedrich M.
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Technische Universität Ilmenau, Institute of Mathematics, Weimarer Straße 25, Ilmenau,D-98693, GermanyDepartment of Applied Mathematics and Computer Science, Technical University of Denmark, Building 303, Lyngby,2800, Denmark
Philipp, Friedrich M.
Stoeva, Diana
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Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, Vienna,1090, AustriaDepartment of Applied Mathematics and Computer Science, Technical University of Denmark, Building 303, Lyngby,2800, Denmark