On multiresolution analysis (MRA) wavelets in ℝ n

Qing Gu; Deguang Han

doi:10.1007/bf02510148

journal article Jul 01, 2000

On multiresolution analysis (MRA) wavelets in ℝ n

Qing Gu

Deguang Han

Journal of Fourier Analysis and Applications Vol. 6 No. 4 pp. 437-447 · Springer Science and Business Media LLC

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References

17

[1]

Baggett, L., Carey, A., Moran, W., and Ohring, P. (1995). Generalized existence theorems for orthonormal wavelets, an abstract approach,Pub. Res. Inst. Math. Sci. Kyoto Univ.,31, 95–111. 10.2977/prims/1195164793

[2]

Baggett, L., Medina, H., and Merrill, K. Generalized multiresolution analysis, and a construction procedure for all wavelets sets in ℝ n ,J. Fourier Anal. Appl., to appear.

[3]

Calogero, A. (1999). Wavelets on general lattices associated with general expanding maps of ℝ n .ERA Am. Math. Soc.,5, 1–10.

[4]

Belogay, E. and Wang, W. (1999). Arbitrary smooth orthogonal nonseparable wavelets in ℝ n ,SIAM J. Math. Anal.,30, 678–697. 10.1137/s0036141097327732

[5]

Cohen, A. and Daubechies, I. (1993). Non-separable bidimensional wavelets bases,Rev. Math. Iberoamericana,9, 51–137. 10.4171/rmi/133

[6]

Dai, X. and Larson, D. (1998). Wandering vectors for unitary systems and orthogonal wavelets,Memoirs Amer. Math. Soc.,640. 10.1090/memo/0640

[7]

Dai, X., Larson, D., and Speegle, D. (1997). Wavelet sets in ℝ n ,J. Fourier Anal. Appl.,3, 451–456. 10.1007/bf02649106

[8]

Dai, X., Larson, D., and Speegle, D. (1998). Wavelet sets in ℝ n II,Contemp. Math.,216, 15–40. 10.1090/conm/216/02962

[9]

Dai, X. and Lu, S. (1996). Wavelets in subspaces,Mich. J. Math.,43, 81–89. 10.1307/mmj/1029005391

[10]

Fang, X. and Wang, X. (1996). Construction of minimally supported frequency (MSF) wavelets,J. Fourier Anal. Appl.,2, 315–327.

[11]

Gu, Q., Larson, D., and Speegle, D. Single-function cyclic dyadic MRA wavelets in ℝ n , preprint.

[12]

Tight compactly supported wavelet frames of arbitrarily high smoothness

Karlheinz Gröchenig, Amos Ron

Proceedings of the American Mathematical Society 1998 10.1090/s0002-9939-98-04232-4

[13]

Han, D. (1997).Unitary Systems, Wavelets and Operator Algebras, Ph.D. Thesis, Texas A&M University.

[14]

Hernandez, E., Wang, X., and Weiss, G. (1996). Smoothing minimally supported (MSF) wavelets: Part I,J. Fourier Anal. Appl.,2, 329–340.

[15]

Hernandez, E., Wang, X., and Weiss, G. (1997). Smoothing minimally supported (MSF) wavelets: Part II,J. Fourier Anal. Appl.,3, 23–41. 10.1007/bf02647945

[16]

Madych, W.R. (1992). Some Elementary Properties of Multiresolution Analysis ofL 2ℝ n , Wavelets: A Tutorial in Theory and Applications, Chui, C.K., Ed., Academic Press, New York.

[17]

Strichartz, R.S. (1994).Construction of Orthonormal Wavelets, Wavelets: Mathematics and Applications. Benedetto, J.J. and Frazier, M.W., Eds., CRC Press, Boca Raton, FL, 23–50.

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References

Details

Published: Jul 01, 2000
Vol/Issue: 6(4)
Pages: 437-447
License: View

Authors

Q

Qing Gu

State Key Laboratory of Organometallic Chemistry, Center for Excellence in Molecular Synthesis, Shanghai Institute of Organic Chemistry, University of Chinese Academy of Sciences, Chinese Academy of Sciences, 345 Lingling Lu, Shanghai 200032, China

D

Deguang Han

Cite This Article

Qing Gu, Deguang Han (2000). On multiresolution analysis (MRA) wavelets in ℝ n. Journal of Fourier Analysis and Applications, 6(4), 437-447. https://doi.org/10.1007/bf02510148

On multiresolution analysis (MRA) wavelets in ℝ n

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