Frame representations for group-like unitary operator systems

    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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