Subspace Weyl-Heisenberg frames

    Authors

    J. P. Gabardo;D. G. Han

    Comments

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    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

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