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The s-elementary wavelets are path-connected
Author(s):
D.
M.
Speegle
Journal:
Proc. Amer. Math. Soc.
127
(1999),
223-233.
MSC (1991):
Primary 46C05;
Secondary 28D05, 42C15
MathSciNet review:
1468204
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Abstract:
A construction of wavelet sets containing certain subsets of  is given. The construction is then modified to yield a continuous dependence on the underlying subset, which is used to prove the path-connectedness of the s-elementary wavelets. A generalization to  is also considered.
References:
- [C]
- C. K. Chui, An Introduction to Wavelets, Acad. Press, New York, 1992. MR 93f:42055
- [DL]
- X. Dai and D. Larson, Wandering vectors for unitary systems and orthogonal wavelets, Mem. Amer. Math. Soc., to appear. CMP 97:07
- [DLS]
- X. Dai, D. Larson and D. Speegle, Wavelets in
 , J. Fourier Anal. Appl. 3 (1997), 451-456. CMP 97:17 - [FW]
- X. Fang and X. Wang, Construction of minimally supported frequency wavelets, J. Fourier Anal. Appl. 2 (1996), no. 4, 315-327. MR 97d:42030
- [H]
- P. Halmos, A Hilbert Space Problem Book, second ed., Springer-Verlag, New York, 1982. MR 84e:47001
- [HWW1]
- E. Hernandez, X. Wang and G. Weiss, Smoothing minimally supported wavelets. I, J. Fourier Anal. Appl. 2 (1996), no. 2, 329-340. MR 97h:42015
- [HWW2]
- E. Hernandez, X. Wang and G. Weiss, Smoothing minimally supported wavelets. II, J. Fourier Anal. Appl. 2 (1997), no. 1, 23-41. CMP 97:06
- [S]
- Darrin Speegle, S-elementary wavelets and the into
 extension property, Dissertation, Texas A&M University.
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Additional Information:
D.
M.
Speegle
Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843
Address at time of publication:
Department of Mathematics, Saint Louis University, St. Louis, Missouri 63103
Email:
speegle@math.tamu.edu
DOI:
10.1090/S0002-9939-99-04555-4
PII:
S 0002-9939(99)04555-4
Received by editor(s):
December 11, 1995
Received by editor(s) in revised form:
May 13, 1997
Additional Notes:
The author was supported in part by the NSF through the Workshop in Linear Analysis and Probability.
Communicated by:
J. Marshall Ash
Copyright of article:
Copyright
1999,
American Mathematical Society
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