Title

Subspace Weyl-Heisenberg Frames

Keywords

Group-like unitary systems; Subspace WH frames; Von Neumann algebras; Weyl-Heisenberg systems

Abstract

A Weyl-Heisenberg frame (WH frame) for L2 (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 ∈ L2(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 L2 (ℝ) space.

Publication Date

1-1-2001

Publication Title

Journal of Fourier Analysis and Applications

Volume

7

Issue

4

Number of Pages

419-433

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/bf02514505

Socpus ID

0347746357 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0347746357

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