Pointwise convergence of a class of non-orthogonal wavelet expansions
HTML articles powered by AMS MathViewer
- by Ahmed I. Zayed PDF
- Proc. Amer. Math. Soc. 128 (2000), 3629-3637 Request permission
Abstract:
Non-orthogonal wavelet expansions associated with a class of mother wavelets is considered. This class of wavelets comprises mother wavelets that are not necessarily integrable over the whole real line, such as Shannon’s wavelet. The pointwise convergence of these wavelet expansions is investigated. It is shown that, unlike other wavelet expansions, the ones under consideration do not necessarily converge pointwise to the functions at points of continuity, unless a more stringent condition, such as bounded variation, is imposed.References
- Ingrid Daubechies, Ten lectures on wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 61, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992. MR 1162107, DOI 10.1137/1.9781611970104
- Susan E. Kelly, Mark A. Kon, and Louise A. Raphael, Pointwise convergence of wavelet expansions, Bull. Amer. Math. Soc. (N.S.) 30 (1994), no. 1, 87–94. MR 1248218, DOI 10.1090/S0273-0979-1994-00490-2
- S. E. Kelly, M. A. Kon, and L. A. Raphael, Local convergence for wavelet expansions, J. Funct. Anal. 126 (1994), no. 1, 102–138. MR 1305065, DOI 10.1006/jfan.1994.1143
- Y. Meyer, Ondelettes, Herman, Paris (1990).
- E. Titchmarsh, Introduction to the Theory of Fourier Integrals, Oxford University Press, United Kingdom (1937).
- Gilbert G. Walter, Pointwise convergence of wavelet expansions, J. Approx. Theory 80 (1995), no. 1, 108–118. MR 1308596, DOI 10.1006/jath.1995.1006
- A. I. Zayed and G. Walter, Wavelets in closed forms, to appear.
Additional Information
- Ahmed I. Zayed
- Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
- Email: zayed@pegasus.cc.ucf.edu
- Received by editor(s): June 16, 1998
- Received by editor(s) in revised form: February 24, 1999
- Published electronically: June 7, 2000
- Communicated by: Christopher D. Sogge
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 3629-3637
- MSC (1991): Primary 42C15, 42C05; Secondary 40A05, 40A30
- DOI: https://doi.org/10.1090/S0002-9939-00-05506-4
- MathSciNet review: 1695334