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abc-Problem for Gabor Systems

Xin-Rong Dai
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      A longstanding problem in Gabor theory is to identify time-frequency shifting lattices $a\mathbb{Z}\times b\mathbb{Z}$ and ideal window functions $\chiI$ on intervals $I$ of length $c$ such that $\{e^{-2\pi i n bt} \chiI(t- m a):\ (m, n)\in \mathbb{Z}\times \mathbb{Z}\}$ 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 $abc$-problem for Gabor systems.
      Format: Paperback / softback CONTRIBUTORS: Xin-Rong Dai EAN: 9781470420154 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2016-11-01 CITY: GENRE: MATHEMATICS / Infinity WIDTH: 178 cm SPINE:

      Book Themes:

      Functional analysis and transforms

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      Xin-Rong Dai, Sun Yat-sen University, Guangzhou, China.Qiyu Sun, University of Central Florida, Orlando, Florida, USA.
      A longstanding problem in Gabor theory is to identify time-frequency shifting lattices $a\mathbb{Z}\times b\mathbb{Z}$ and ideal window functions $\chiI$ on intervals $I$ of length $c$ such that $\{e^{-2\pi i n bt} \chiI(t- m a):\ (m, n)\in \mathbb{Z}\times \mathbb{Z}\}$ 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 $abc$-problem for Gabor systems.
      Format: Paperback / softback CONTRIBUTORS: Xin-Rong Dai EAN: 9781470420154 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2016-11-01 CITY: GENRE: MATHEMATICS / Infinity WIDTH: 178 cm SPINE:

      Book Themes:

      Functional analysis and transforms

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      Be the first to write a review
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      Xin-Rong Dai, Sun Yat-sen University, Guangzhou, China.Qiyu Sun, University of Central Florida, Orlando, Florida, USA.

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