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abc-problem for Gabor systems / Xin-Rong Dai and Qiyu Sun.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 244, no 1152.Publication details: Providence : American Mathematical Society, 2016.Description: ix, 99 pages : illustrations ; 26 cmISBN:
  • 9781470420154 (alk. paper)
Subject(s): Additional physical formats: Online version:: Abc-problem for Gabor systemsDDC classification:
  • 510 23 Am512
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: 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.
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Includes bibliographical references and index.

* 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

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.

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