Title

Frame representations for group-like unitary operator systems

Authors

Authors

J. P. Gabardo;D. G. Han

Abbreviated Journal Title

J. Operat. Theor.

Keywords

group-like unitary systems; Gabor systems; frame vectors; von Neumann; algebras; frame representations; analysis operators; ALGEBRAS; Mathematics

Abstract

A group-like unitary system U is a set of unitary operators such that the group generated by the system is contained in TU, where T denotes the unit circle. Every frame representation for a group-like unitary system is (unitarily equivalent to) a subrepresentation of its left regular representation and the norm of a normalized tight frame vector determines the redundancy of the representation. In the case that a group-like unitary system admits enough Bessel vectors, the commutant of the system can be characterized in terms of the analysis operators associated with all the Bessel vectors. This allows us to define a natural quantity (the frame redundancy) for the system which will determine when the system admits a cyclic vector. A simple application of this leads to an elementary proof to the well-known time-frequency density theorem in Gabor analysis.

Journal Title

Journal of Operator Theory

Volume

49

Issue/Number

2

Publication Date

1-1-2003

Document Type

Article

Language

English

First Page

223

Last Page

244

WOS Identifier

WOS:000184621700001

ISSN

0379-4024

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