Frames and generalized shift-invariant systems

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedings – Annual report year: 2004Researchpeer-review

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With motivation from the theory of Hilbert-Schmidt operators we review recent topics concerning frames in L 2 (R) and their duals. Frames are generalizations of orthonormal bases in Hilbert spaces. As for an orthonormal basis, a frame allows each element in the underlying Hilbert space to be written as an unconditionally convergent infinite linear combination of the frame elements; however, in contrast to the situation for a basis, the coefficients might not be unique. We present the basic facts from frame theory and the motivation for the fact that most recent research concentrates on tight frames or dual frame pairs rather than general frames and their canonical dual. The corresponding results for Gabor frames and wavelet frames are discussed in detail.
Original languageEnglish
Title of host publicationOPERATOR THEORY : ADVANCES AND APPLICATIONS : Pseudo-Differential Operators and Related Topics
VolumeVolume 164
PublisherBirkhäuser Verlag
Publication date2004
ISBN (Print)37-64-37513-2
Publication statusPublished - 2004
EventInternational Conference on Pseudo-Differential Operators and Related Topics - Vaxjo Univ, Vaxjo, SWEDEN
Duration: 1 Jan 2004 → …


ConferenceInternational Conference on Pseudo-Differential Operators and Related Topics
CityVaxjo Univ, Vaxjo, SWEDEN
Period01/01/2004 → …

ID: 4603874