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  Current Development in Theory and Applications of Wavelets  
 ISSN: 0973-5607
 
 
 

     Current Development in Theory and Applications of Wavelets
    Volume 1, Issue 3, Pages 273 - 292 (December 2007)


MULTILEVEL DECOMPOSITION IN A HILBERT SPACE

Somdeb Majumdar (USA), Nhan Levan (USA) and Carlos S. Kubrusly (Brazil)

Received September 14, 2007

References:



[1] I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 61, SIAM, Philadelphia, 1992.

[2] P. Flandrin, Time-Frequency/Time-Scale Analysis, Academic Press, San Diego, 1999.

[3] P. R. Halmos, Shifts on Hilbert spaces, J. Reine Angew. Math. 208 (1961), 102-112.

[4] E. Hernandez and G. Weiss, A First Course on Wavelets, CRC Press, Boca Raton, 1996.

[5] F. Keinert, Wavelets and Multiwavelets, CRC Press, Boca Raton, 2004.

[6] C. S. Kubrusly, Hilbert Space Operators, Birkhäuser, Boston, 2003.

[7] C. S. Kubrusly and N. Levan, Abstract wavelets generated by Hilbert space shift operators, Adv. Math. Sci. Appl. 16 (2006), 643-660.

[8] N. Levan and C. S. Kubrusly, Multiresolution approximation scale and time-shift subspaces, Multidimens. Syst. Signal Process 17 (2006), 343-354.

[9] S. Majumdar, New Approach to Operator-Theoretic Frameworks for Wavelet Multiresolution Approximation and Analysis, Ph.D. Dissertation, Department of Electrical Engineering, UCLA, Los Angeles, June 2006.

[10] S. G. Mallat, Multiresolution approximations and wavelet orthonormal bases of Trans. Amer. Math. Soc. 315 (1989), 69-87.

[11] Y. Meyer, Ondelettes et Functions Spline, Séminaire EDP, École Polytechnique, Paris, 1986.

[12] B. Sz.-Nagy and C. Foias, Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam, 1970.

Keywords and phrases: multilevel decomposition, multilevel approximation, multiresolution approximation, scaling operators, time-varying shifts on

 


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