Parseval frames for ICC groups

    Authors

    D. E. Dutkay; D. G. Han;G. Picioroaga

    Comments

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    Abbreviated Journal Title

    J. Funct. Anal.

    Keywords

    Parseval frames; Kadison-Singer problem; Undersampling; II(1)-factors; KADISON-SINGER PROBLEM; ABELIAN-GROUPS; GABOR FRAMES; REPRESENTATIONS; MATHEMATICS

    Abstract

    We analyze Parseval frames generated by the action of an ICC group on a Hilbert space. We parametrize the set of all such Parseval frames by operators in the commutant of the corresponding representation. We characterize when two Such frames are strongly disjoint. We prove an undersampling result showing that if the representation has a Parseval frame of equal norm vectors of norm 1/root N, the Hilbert space is spanned by an orthonormal basis generated by a subgroup. As applications we obtain some sufficient conditions under which a unitary representation admits a Parseval frame which is spanned by a Riesz sequences generated by a subgroup. In particular, every subrepresentation of the left-regular representation of a free group has this property. Published by Elsevier Inc.

    Journal Title

    Journal of Functional Analysis

    Volume

    256

    Issue/Number

    9

    Publication Date

    1-1-2009

    Document Type

    Article

    Language

    English

    First Page

    3071

    Last Page

    3090

    WOS Identifier

    WOS:000265126800013

    ISSN

    0022-1236

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