Journal article

Publication year: 2004

Pages: 383-408

Journal: Journal of Fourier Analysis and Applications

Volume number: 10

Issue number: 4

ISSN: 1069-5869

eISSN: 1531-5851

DOI Link: https://doi.org/10.1007/s00041-004-3024-7

Publisher: Springer

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.

Harvard Citation style: Casazza, P., Kutyniok, G. and Lammers, M. (2004) Duality principles in frame theory, Journal of Fourier Analysis and Applications, 10(4), pp. 383-408. https://doi.org/10.1007/s00041-004-3024-7

APA Citation style: Casazza, P., Kutyniok, G., & Lammers, M. (2004). Duality principles in frame theory. Journal of Fourier Analysis and Applications. 10(4), 383-408. https://doi.org/10.1007/s00041-004-3024-7