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The abc-problem for Gabor systems /
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 \{e^{-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 al...
| Clasificación: | Libro Electrónico |
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| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
2016.
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| Colección: | Memoirs of the American Mathematical Society ;
no. 1152. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | 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 \{e^{-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. |
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| Notas: | "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. |
| Descripción Física: | 1 online resource (ix, 99 pages) : illustrations |
| Bibliografía: | Includes bibliographical references (pages 97-99). |
| ISBN: | 9781470435042 1470435047 1470420155 9781470420154 |
| ISSN: | 0065-9266 ; |