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Necessary and sufficient conditions for expansions of Gabor type |
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| Authors: | Kunchuan Wang |
| Affiliation: | 1. Department of Mathematics National Hualien, University of Education, 970, Hua-Lien, Taiwan, ROC |
| Abstract: | In this paper, we give necessary and sufficient conditions for two families of Gabor functions of a certain type to yield a reproducing identity on L2(Rn). As applications, we characterize when such families yield orthonormal or bi-orthogonal expansions. We also obtain a generalization of the Balian-Low theorem for general reproducing identities (not necessary coming from a frame). |
| Keywords: | Balian- Low theorem bi-orthogonal expansion orthogonal expansion Gabor expansion wavelet TYPE GABOR frame generalization theorem identities characterize orthonormal applications sufficient conditions Gabor functions type yield identity paper |
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