|
On the dimension function of orthonormal wavelets
Author(s):
Manos
Papadakis
Journal:
Proc. Amer. Math. Soc.
128
(2000),
2043-2049.
MSC (1991):
Primary 41A15, 41A30, 42A38, 42C15, 46N99
Posted:
November 1, 1999
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We announce the following result: Every orthonormal wavelet of  is associated with a multiresolution analysis such that for the subspace  the integral translates of a countable at most family of functions is a tight frame.
References:
- 1.
- P.Auscher, Solution of two problems on wavelets, The J. Geometric Anal. 5 nr 2, pp. 181-236, 1995. MR 96g:42016
- 2.
- J. Benedetto, S. Li, The theory of multiresolution analysis frames and applications to filter banks, Appl. Comput. Harmon. Anal. 5 (1998), no. 4, 380-427. CMP 99:02
- 3.
- L.W. Baggett, H.A. Medina, K.D. Merrill, Generalized multiresolution analyses and a construction procedure for all wavelet sets in
 , preprint, 1998. - 4.
- D. Han, D.R. Larson, Frames, bases and group representations, to appear Memoirs AMS.
- 5.
- E. Hernández, G. Weiss, A first course on wavelets, CRC Press, Boca Raton FL, 1996. MR 97i:42015
- 6.
- G. Gripenberg, A necessary and sufficient condition for the existence of a father wavelet, Studia Mathematica 114(3), pp.207-226, 1995. MR 96d:42049
- 7.
- X. Wang, The study of wavelets from the properties of their Fourier transforms, Ph.D. Thesis, Washington University in St. Louis, 1995.
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(1991):
41A15, 41A30, 42A38, 42C15, 46N99
Retrieve articles in all Journals with MSC
(1991):
41A15, 41A30, 42A38, 42C15, 46N99
Additional Information:
Manos
Papadakis
Affiliation:
Department of Informatics, University of Athens, Panepistimiopolis, GR-15784 Zografou, Greece
Address at time of publication:
Department of Mathematics, University of Houston, Houston, Texas 77204-3476
Email:
mpapad@di.uoa.gr, mpapadak@math.uh.edu
DOI:
10.1090/S0002-9939-99-05256-9
PII:
S 0002-9939(99)05256-9
Keywords:
Multiresolution analysis,
wavelets,
dimension function,
frames.
Received by editor(s):
June 15, 1998
Received by editor(s) in revised form:
August 25, 1998
Posted:
November 1, 1999
Communicated by:
David R. Larson
Copyright of article:
Copyright
2000,
American Mathematical Society
|
Comments: webmaster@ams.org