Subspace Weyl-Heisenberg frames
Abbreviated Journal Title
J. Fourier Anal. Appl.
group-like unitary systems; von Neumann algebras; Weyl-Heisenberg; systems; subspace WH frames; WAVELET; Mathematics, Applied
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  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 of Fourier Analysis and Applications
"Subspace Weyl-Heisenberg frames" (2001). Faculty Bibliography 2000s. 7999.