Frames and generalized shift-invariant systems. (English) Zbl 1104.42018
Boggiatto, Paolo (ed.) et al., Pseudo-differential operators and related topics. Papers based on lectures given at the international conference, Växjö University, Sweden, June 22 to June 25, 2005. Basel: Birkhäuser (ISBN 3-7643-7513-2/hbk). Operator Theory: Advances and Applications 164, 193-209 (2006).
A countable family is called a frame for if there exist constants , such that, for all , . We say that a frame is tight if .
The paper under review is based on a lecture given at the Växjö University, Sweden, in 2005. It provides a motivation for the study of frames in and their duals. Basic facts from the frame theory are followed by a discussion of 3 types of frames: Gabor frames, wavelet frames, and generalized shift-invariant frames. The aim of this paper is to present advantages of using tight frames over general frames.
|42C15||General harmonic expansions, frames|
|42C40||Wavelets and other special systems|