| Description |
1 online resource (ix, 99 pages) : illustrations |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; volume 244, number 1152 |
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Memoirs of the American Mathematical Society ; no. 1152.
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| Contents |
Introduction -- Gabor frames and infinite matrices -- Maximal invariant sets -- Piecewise linear transformations -- Maximal invariant sets with irrational time shifts -- Maximal invariant sets with rational time shifts -- The abc-problem for Gabor systems -- Appendix A. Algorithm -- Appendix B. Uniform sampling of signals in a shift-invariant space -- Bibliography |
| Summary |
A longstanding problem in Gabor theory is to identify time-frequency shifting lattices a\mathbb{Z}\times b\mathbb{Z} and ideal window functions \chi_I on intervals I of length c such that \{ê{-2\pi i n bt} \chi_I(t- m a):\ (m, n)\in \mathbb{Z}\times \mathbb{Z}\} are Gabor frames for the space of all square-integrable functions on the real line. In this paper, the authors create a time-domain approach for Gabor frames, introduce novel techniques involving invariant sets of non-contractive and non-measure-preserving transformations on the line, and provide a complete answer to the above abc-pro |
| Notes |
"Volume 244, number 1152 (first of 4 numbers), November 2016." |
|
Keywords: abc problem for Gabor systems, Gabor frames, infinite matrices, piecewise linear transformation, ergodic theorem, sampling, shift-invariant spaces |
| Bibliography |
Includes bibliographical references (pages 97-99) |
| Notes |
Print version record |
| Subject |
Wavelets (Mathematics)
|
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Gabor transforms.
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Matrices.
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Gabor transforms
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Matrices
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Wavelets (Mathematics)
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| Form |
Electronic book
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| Author |
Sun, Qiyu, 1966- author.
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American Mathematical Society, publisher
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| LC no. |
2016035445 |
| ISBN |
9781470435042 |
|
1470435047 |
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1470420155 |
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9781470420154 |
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