Title

Subspace Weyl-Heisenberg frames

Authors

Authors

J. P. Gabardo;D. G. Han

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

J. Fourier Anal. Appl.

Keywords

group-like unitary systems; von Neumann algebras; Weyl-Heisenberg; systems; subspace WH frames; WAVELET; Mathematics, Applied

Abstract

A Weyl-Heisenberg frame (WH frame) for L-2(R) allows every square integrable function on the line to be decomposed into the infinite sum of linear combination of translated and modulated versions of a fixed function. Some sufficient conditions for g epsilon L-2(R) to be a subspace Weyl-Heisenberg frame were given in a recent work [3] by Casazza and Christensen. Obviously every invariant subspace (under translation and modulation) is cyclic if it has a subspace WH frame. In the present article we prove that the cyclicity property is also sufficient for a subspace to admit a WH frame. We also investigate the dilation property for subspace Weyl-Heisenberg frames and show that every normalized tight subspace WH frame can be dilated to a normalized tight WH frame which is "maximal" In other words, every subspace WH frame is the compression of a WH frame which cannot be dilated anymore within the L-2(R) space.

Journal Title

Journal of Fourier Analysis and Applications

Volume

7

Issue/Number

4

Publication Date

1-1-2001

Document Type

Article

Language

English

First Page

419

Last Page

433

WOS Identifier

WOS:000169514700006

ISSN

1069-5869

Share

COinS