New Proof for Balian-Low Theorem of Nonlinear Gabor System
The main purpose of this paper is to give a new proof of the Balian-Low theorem for Gabor system {eimθ(2πt)g(t−n), m,n∈ℤ}, which is proposed by Fu et al. and associated with nonlinear Fourier atoms. To this end, we establish the relationships between spaces L2(ℝ,dθ) and L2(ℝ). We also introduce the...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/530172 |
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| _version_ | 1832552719003418624 |
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| author | D. H. Yuan S. Z. Yang X. W. Zheng Y. F. Shen |
| author_facet | D. H. Yuan S. Z. Yang X. W. Zheng Y. F. Shen |
| author_sort | D. H. Yuan |
| collection | DOAJ |
| description | The main purpose of this paper is to give a new proof of the Balian-Low
theorem for Gabor system {eimθ(2πt)g(t−n), m,n∈ℤ}, which is proposed by Fu et al. and associated with nonlinear Fourier atoms. To this end, we establish the relationships between spaces L2(ℝ,dθ) and L2(ℝ). We also introduce the concept of frame associated with nonlinear Fourier atoms for L2(ℝ,dθ) and obtain many subsidiary results for this kind of (Gabor) frames. |
| format | Article |
| id | doaj-art-7bcc71b40ffe47fc930f341f7eb157fa |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-7bcc71b40ffe47fc930f341f7eb157fa2025-02-03T05:58:05ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/530172530172New Proof for Balian-Low Theorem of Nonlinear Gabor SystemD. H. Yuan0S. Z. Yang1X. W. Zheng2Y. F. Shen3Department of Mathematics, Hanshan Normal University, Chaozhou, Guangdong 521041, ChinaDepartment of Mathematics, Shantou University, Shantou, Guangdong 515063, ChinaDepartment of Mathematics, Shantou University, Shantou, Guangdong 515063, ChinaDepartment of Mathematics, Shantou University, Shantou, Guangdong 515063, ChinaThe main purpose of this paper is to give a new proof of the Balian-Low theorem for Gabor system {eimθ(2πt)g(t−n), m,n∈ℤ}, which is proposed by Fu et al. and associated with nonlinear Fourier atoms. To this end, we establish the relationships between spaces L2(ℝ,dθ) and L2(ℝ). We also introduce the concept of frame associated with nonlinear Fourier atoms for L2(ℝ,dθ) and obtain many subsidiary results for this kind of (Gabor) frames.http://dx.doi.org/10.1155/2013/530172 |
| spellingShingle | D. H. Yuan S. Z. Yang X. W. Zheng Y. F. Shen New Proof for Balian-Low Theorem of Nonlinear Gabor System Journal of Function Spaces and Applications |
| title | New Proof for Balian-Low Theorem of Nonlinear Gabor System |
| title_full | New Proof for Balian-Low Theorem of Nonlinear Gabor System |
| title_fullStr | New Proof for Balian-Low Theorem of Nonlinear Gabor System |
| title_full_unstemmed | New Proof for Balian-Low Theorem of Nonlinear Gabor System |
| title_short | New Proof for Balian-Low Theorem of Nonlinear Gabor System |
| title_sort | new proof for balian low theorem of nonlinear gabor system |
| url | http://dx.doi.org/10.1155/2013/530172 |
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