Operators and Frames
نویسندگان
چکیده
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.
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