Title

Parseval frames for ICC groups

Authors

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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