Proof of the HRT conjecture for (2, 2) configurations

Ciprian Demeter, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review

Abstract

We prove a particular case of the so-called "HRT conjecture". More precisely, we show that given any planar trapezoid with vertices (tjj)j=14∈R{double-struck}2 and given any nontrivial L2(R{double-struck}) function f, there is no linear dependence between the time-frequency translates f(x+tj)e2πiξjx. Our methods are mostly number theoretical.

Original languageEnglish (US)
Pages (from-to)151-159
Number of pages9
JournalJournal of Mathematical Analysis and Applications
Volume388
Issue number1
DOIs
StatePublished - Apr 1 2012

Keywords

  • Diophantine approximation
  • HRT conjecture
  • Time-frequency translates
  • Trigonometric polynomials

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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