Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the existence and constructions of orthonormal wavelets on $L_2(\mathbb R^s)$

Author: Chen Di-Rong
Journal: Proc. Amer. Math. Soc. 125 (1997), 2883-2889
MSC (1991): Primary 41A63, 42C05, 46C99
MathSciNet review: 1396974
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For a multiresolution analysis of $L _2 (\mathbb {R}^ s)$ associated with the scaling matrix $T$ having determinant $n$ we prove the existence of a wavelet basis with certain desirable properties if $2n-1 >s$ and its real-valued counterpart if the scaling function is real-valued and $n - 1 > s$. That those results cannot be extended to $2n - 1 \leq s$ and $n -1 \leq s$ respectively in general is demonstrated by Adams’s theorem about vector fields on spheres. Moreover we present some new explicit constructions of wavelets, among which is a variation of Riemenschneider-Shen’s method for $s\leq 3 .$

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 41A63, 42C05, 46C99

Retrieve articles in all journals with MSC (1991): 41A63, 42C05, 46C99

Additional Information

Chen Di-Rong
Affiliation: Department of Applied Mathematics, Beijing University of Aeronautics and Astronautics, Beijing 100083, People’s Republic of China

Received by editor(s): January 31, 1994
Received by editor(s) in revised form: April 9, 1996
Additional Notes: Research supported in part by Natural Science Foundation of China.
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1997 American Mathematical Society