Duality Principles in Frame Theory

Casazza, Peter G.; Kutyniok, Gitta und Lammers, Mark C. (July 2004): Duality Principles in Frame Theory. In: Journal of Fourier Analysis and Applications, Vol. 10: pp. 383-408

Abstract

Duality principles in Gabor theory such as the Ron–Shen duality principle and the Wexler–Raz biorthogonality relations play a fundamental role for analyzing Gabor systems. In this article we present a general approach to derive duality principles in abstract frame theory. For each sequence in a separable Hilbert space we define a corresponding sequence dependent only on two orthonormal bases. Then we characterize exactly properties of the first sequence in terms of the associated one, which yields duality relations for the abstract frame setting. In the last part we apply our results to Gabor systems.

• 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: 1069-5869
• Language: English