Journal of Operator Theory

Volume 70, Issue 1, Summer 2013 pp. 145-164.

Operators and frames

Authors: Jameson Cahill (1), Peter G. Casazza (2), and Gitta Kutyniok (3)
Author institution: (1) Department of Mathematics, University of Missouri, Columbia, MO 65211, U.S.A.
(2) Department of Mathematics, University of Missouri, Columbia, MO 65211, U.S.A.
(3) Institute of Mathematics, Technische Universitat Berlin, 10623 Berlin, Germany

Summary: Hilbert space frame theory has applications to various areas of pure mathematics, applied mathematics, and engineering. However, the question of how applying an invertible operator to a frame changes its properties has not yet been satisfactorily answered, and only partial results are known to date. In this paper, we will provide a comprehensive study of those questions, and, in particular, prove characterization results for (1) operators which generate frames with a prescribed frame operator; (2) operators which change the norms of the frame vectors by a constant multiple; (3) operators which generate equal norm nearly Parseval frames.

DOI: http://dx.doi.org/10.7900/jot.2011may10.1973
Keywords: analysis operator, frame operator, Hilbert space frame, synthesis operator

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