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Translates of Functions on the Heisenberg Group and the HRT Conjecture

Part of: Abstract harmonic analysis Nontrigonometric harmonic analysis Lie groups

Published online by Cambridge University Press:  03 February 2020

B. Currey  and
V. Oussa
B. Currey
Affiliation:
Department of Mathematics and Statistics, St. Louis University, St. Louis, MO63103 Email: bradley.currey@slu.edu
V. Oussa
Affiliation:
Department of Mathematics and Computer Science, Bridgewater State University, Bridgewater, MA02324 Email: voussa@bridgew.edu
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Abstract

We prove that the HRT (Heil, Ramanathan, and Topiwala) Conjecture is equivalent to the conjecture that co-central translates of square-integrable functions on the Heisenberg group are linearly independent.

Keywords

Heisenberg groupHRT conjectureGabor systemtime-frequency system

MSC classification

Primary: 42C40: Wavelets and other special systems
Secondary: 43A80: Analysis on other specific Lie groups 22E25: Nilpotent and solvable Lie groups

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 4 , December 2020 , pp. 871 - 881
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Copyright
© Canadian Mathematical Society 2020

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