TY - JOUR

T1 - Proof of the HRT conjecture for (2, 2) configurations

AU - Demeter, Ciprian

AU - Zaharescu, Alexandru

N1 - Funding Information:
E-mail addresses: demeterc@indiana.edu (C. Demeter), zaharesc@math.uiuc.edu (A. Zaharescu). 1 The first author is supported by a Sloan Research Fellowship and by NSF Grants DMS-0742740 and 0901208. 2 The second author is supported by NSF Grant DMS-0901621.

PY - 2012/4/1

Y1 - 2012/4/1

N2 - We prove a particular case of the so-called "HRT conjecture". More precisely, we show that given any planar trapezoid with vertices (tj,ξj)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.

AB - We prove a particular case of the so-called "HRT conjecture". More precisely, we show that given any planar trapezoid with vertices (tj,ξj)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.

KW - Diophantine approximation

KW - HRT conjecture

KW - Time-frequency translates

KW - Trigonometric polynomials

UR - http://www.scopus.com/inward/record.url?scp=84455202334&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84455202334&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2011.11.030

DO - 10.1016/j.jmaa.2011.11.030

M3 - Article

AN - SCOPUS:84455202334

VL - 388

SP - 151

EP - 159

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -