TY - JOUR
T1 - Quasi-orthogonal decompositions of structured frames
AU - Fornasier, Massimo
N1 - Funding Information:
E-mail address: [email protected]. 1 The author has been supported by an Österreich-Stipendium awared by ÖAD/BAMO on behalf of the Federal Ministery for Education, Science and Culture (BMBWK), Austria 0022-247X/$ – see front matter 2003 Elsevier Inc. All rights reserved. doi:10.1016/j.jmaa.2003.09.041
PY - 2004/1/1
Y1 - 2004/1/1
N2 - A decomposition of a Hilbert space Hscr; into a quasi-orthogonal family of closed subspaces is introduced. We shall investigate conditions in order to derive bounded families of corresponding quasi-projectors or resolutions of the identity operator. Given a local family of atoms, or generalized stable basis, for each subspace, we show that the union of the local atoms can generate a global frame for the Hilbert space. Corresponding duals can be calculated in a flexible way by means of systems of quasi-projectors. An application to Gabor frames is presented as example of the use of this technique, for calculation of duals and explicit estimates of lattice constants.
AB - A decomposition of a Hilbert space Hscr; into a quasi-orthogonal family of closed subspaces is introduced. We shall investigate conditions in order to derive bounded families of corresponding quasi-projectors or resolutions of the identity operator. Given a local family of atoms, or generalized stable basis, for each subspace, we show that the union of the local atoms can generate a global frame for the Hilbert space. Corresponding duals can be calculated in a flexible way by means of systems of quasi-projectors. An application to Gabor frames is presented as example of the use of this technique, for calculation of duals and explicit estimates of lattice constants.
KW - Decomposition methods
KW - Frames
KW - Gabor analysis
KW - Iterative algorithms
KW - Wiener amalgams
UR - http://www.scopus.com/inward/record.url?scp=0346316857&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2003.09.041
DO - 10.1016/j.jmaa.2003.09.041
M3 - Article
AN - SCOPUS:0346316857
SN - 0022-247X
VL - 289
SP - 180
EP - 199
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -