TY - JOUR
TI - Frames and generalized shift-invariant systems
LA - eng
PB - BirkhĂ¤user Verlag
AU - Christensen, Ole
JF - Operator Theory : Advances and Applications
SP - 193
EP - 209
PY - 2004
SN - 3764375132
AB - 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.
ER -