Completeness of Gabor systems

JOURNAL OF APPROXIMATION THEORY

卷:207

Article

Groechenig, Karlheinz¹  Haimi, Antti¹  Romero, Jose Luis¹ 

[1] Univ Vienna, Fac Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

关键词: Gabor system;    Hermite function;    Totally positive function;    Coherent state;    Completeness;    Frame;   

DOI  :  10.1016/j.jat.2016.03.001

来源: Elsevier

【 摘 要 】

We investigate the completeness of Gabor systems with respect to several classes of window functions on rational lattices. Our main results show that the time frequency shifts of every finite linear combination of Hermite functions with respect to a rational lattice are complete in L-2 (IR), thus generalizing a remark of von Neumann (and proved by Bargmann, Perelomov et al.). An analogous result is proven for functions that factor into certain rational functions and the Gaussian. The results are also interesting from a conceptual point of view since they show a vast difference between the completeness and the frame property of a Gabor system. In the terminology of physics we prove new results about the completeness of coherent state subsystems. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free