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Title page for ETD etd-03202019-161148


Type of Document Dissertation
Author Leshen, Sara
URN etd-03202019-161148
Title Balian-Low Type Results for Gabor Schauder Bases
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Alexander Powell Committee Chair
Akram Aldroubi Committee Member
David Smith Committee Member
Doug Hardin Committee Member
Gieri Simonett Committee Member
Keywords
  • Schauder bases
  • uncertainty principle
  • time-frequency analysis
Date of Defense 2019-03-19
Availability unrestricted
Abstract
The uncertainty principle implies that a function and its Fourier transform cannot both be well-localized. The Balian-Low theorem is a version of the uncertainty principle for generators of Gabor orthonormal bases. This dissertation proves a new Balian-Low type theorem for compactly supported generators of Gabor Schauder bases. Moreover, we show that the classical Balian-Low theorem for orthonormal bases does not hold for Schauder bases.
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