Generalized frames and their redundancy
Authors:
A. Askari-Hemmat, M. A. Dehghan and M. Radjabalipour
Journal:
Proc. Amer. Math. Soc. 129 (2001), 1143-1147
MSC (1991):
Primary 42C15, 46C99
DOI:
https://doi.org/10.1090/S0002-9939-00-05689-6
Published electronically:
October 20, 2000
MathSciNet review:
1814151
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Let be a generalized frame in a separable Hilbert space
indexed by a measure space
, and assume its analysing operator is surjective. It is shown that
is essentially discrete; that is, the corresponding index measure space
can be decomposed into atoms
such that
is isometrically isomorphic to the weighted space
of all sequences
of complex numbers with
, where
This provides a new proof for the redundancy of the windowed Fourier transform as well as any wavelet family in
.
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Additional Information
A. Askari-Hemmat
Affiliation:
Department of Mathematics, University of Shiraz, Shiraz, Iran
M. A. Dehghan
Affiliation:
Department of Mathematics, Valiasr University, Rafsanjan, Iran
M. Radjabalipour
Affiliation:
Department of Mathematics, University of Kerman, Kerman, Iran
Email:
radjab@arg3.uk.ac.ir
DOI:
https://doi.org/10.1090/S0002-9939-00-05689-6
Keywords:
Generalized frame,
redundancy,
wavelet,
windowed Fourier transform
Received by editor(s):
February 20, 1998
Received by editor(s) in revised form:
October 12, 1998, and July 10, 1999
Published electronically:
October 20, 2000
Additional Notes:
This research is supported by Mahani Math. Research Center (Kerman, Iran) and ICTP (Trieste, Italy)
Communicated by:
David R. Larson
Article copyright:
© Copyright 2000
American Mathematical Society