caa a22 4500 46324706X CHVBK 20180405153329.0 cr unu---uuuuu 170326e20070401xx s 000 0 eng 10.1007/s00041-006-6073-2 doi (NATIONALLICENCE)springer-10.1007/s00041-006-6073-2 Heil Christopher School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA aut History and Evolution of the Density Theorem for Gabor Frames [Elektronische Daten] [Christopher Heil] The Density Theorem for Gabor Frames is one of the fundamental results of time-frequency analysis. This expository survey attempts to reconstruct the long and very involved history of this theorem and to present its context and evolution, from the one-dimensional rectangular lattice setting, to arbitrary lattices in higher dimensions, to irregular Gabor frames, and most recently beyond the setting of Gabor frames to abstract localized frames. Related fundamental principles in Gabor analysis are also surveyed, including the Wexler-Raz biorthogonality relations, the Duality Principle, the Balian-Low Theorem, the Walnut and Janssen representations, and the Homogeneous Approximation Property. An extended bibliography is included. Birkhauser Boston, 2007 Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/2(2007-04-01), 113-166 1069-5869 13:2<113 2007 13 41 https://doi.org/10.1007/s00041-006-6073-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00041-006-6073-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Heil Christopher School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA aut NATIONALLICENCE 773 0- Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/2(2007-04-01), 113-166 1069-5869 13:2<113 2007 13 41 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer