Operators and Frames

Cahill, Jameson; Casazza, Peter G. und Kutyniok, Gitta (2013): Operators and Frames. In: Journal of Operator Theory, Vol. 70, No. 1: pp. 145-164

Abstract

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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Bavarian Chair for Mathematical Foundations of Artificial Intelligence
• Subjects: 500 Science > 510 Mathematics
• ISSN: 03794024, 18417744
• Language: English