Title of article
Nonharmonic Gabor Expansions
Author/Authors
Hameed Mohammed، N. No Affiliation , Amini، M. Department of Mathematics - Faculty of Mathematical Sciences - Tarbiat Modares University, Tehran, Iran
Issue Information
فصلنامه با شماره پیاپی سال 2014
Pages
9
From page
165
To page
173
Abstract
We consider Gabor systems generated by a Gaussian function and prove certain classical results of Paley and Wiener on nonharmonic Fourier series of complex exponentials for the Gabor expansion. In particular, we prove a version of Plancherel-Po ́lya theorem for entire functions with finite order of growth and use the Hadamard factorization theorem to study regularity, exactness and deficiency of Gabor systems.
Abstract
We consider Gabor systems generated by a Gaussian function and prove certain classical results of Paley and Wiener on nonharmonic Fourier series of complex exponentials for the Gabor expansion. In particular, we prove a version of Plancherel-Po ?lya theorem for entire functions with finite order of growth and use the Hadamard factorization theorem to study regularity, exactness and deficiency of Gabor systems.
Keywords
Gabor system , Nonharmonic Fourier series , Deficiency , Entire functions , Order of growth
Journal title
Journal of Sciences
Serial Year
2014
Journal title
Journal of Sciences
Record number
1589842
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