Characterizations of Irregular Multigenerator Gabor Frame on Periodic Subsets of ℝ
We consider the multigenerator system {EmblTnalφl,m,n∈ℤ, l=0,…,r-1} for φ0,…,φr-1∈L2(𝕊) and a0,b0,…,ar-1, br-1>0, where the parameters b0,…,br-1>0 are not necessary the same. With the help of frame theory, we provide some sufficient or necessary conditions for the system to be a frame for L2(𝕊...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/746823 |
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| author | D. H. Yuan Y. Feng Y. F. Shen S. Z. Yang |
| author_facet | D. H. Yuan Y. Feng Y. F. Shen S. Z. Yang |
| author_sort | D. H. Yuan |
| collection | DOAJ |
| description | We consider the multigenerator system {EmblTnalφl,m,n∈ℤ, l=0,…,r-1} for φ0,…,φr-1∈L2(𝕊) and a0,b0,…,ar-1, br-1>0, where the parameters b0,…,br-1>0 are not necessary the same. With the help of frame theory, we provide some sufficient or necessary conditions for the system to be a frame for L2(𝕊). Moreover, we present some characterizations for this system to be a Parseval frame. |
| format | Article |
| id | doaj-art-240923dd67b74027939b69b9fd217cc6 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-240923dd67b74027939b69b9fd217cc62025-08-20T02:04:40ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/746823746823Characterizations of Irregular Multigenerator Gabor Frame on Periodic Subsets of ℝD. H. Yuan0Y. Feng1Y. F. Shen2S. Z. Yang3Department of Mathematics, Shantou University, Guangdong, Shantou 515063, ChinaDepartment of Mathematics, Shantou University, Guangdong, Shantou 515063, ChinaDepartment of Mathematics, Shantou University, Guangdong, Shantou 515063, ChinaDepartment of Mathematics, Shantou University, Guangdong, Shantou 515063, ChinaWe consider the multigenerator system {EmblTnalφl,m,n∈ℤ, l=0,…,r-1} for φ0,…,φr-1∈L2(𝕊) and a0,b0,…,ar-1, br-1>0, where the parameters b0,…,br-1>0 are not necessary the same. With the help of frame theory, we provide some sufficient or necessary conditions for the system to be a frame for L2(𝕊). Moreover, we present some characterizations for this system to be a Parseval frame.http://dx.doi.org/10.1155/2012/746823 |
| spellingShingle | D. H. Yuan Y. Feng Y. F. Shen S. Z. Yang Characterizations of Irregular Multigenerator Gabor Frame on Periodic Subsets of ℝ Abstract and Applied Analysis |
| title | Characterizations of Irregular Multigenerator Gabor Frame on Periodic Subsets of ℝ |
| title_full | Characterizations of Irregular Multigenerator Gabor Frame on Periodic Subsets of ℝ |
| title_fullStr | Characterizations of Irregular Multigenerator Gabor Frame on Periodic Subsets of ℝ |
| title_full_unstemmed | Characterizations of Irregular Multigenerator Gabor Frame on Periodic Subsets of ℝ |
| title_short | Characterizations of Irregular Multigenerator Gabor Frame on Periodic Subsets of ℝ |
| title_sort | characterizations of irregular multigenerator gabor frame on periodic subsets of r |
| url | http://dx.doi.org/10.1155/2012/746823 |
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