Abstract
In this work, a sort of binary wavelet packages with multi-scale are introduced, which are generalizations of multivariant wavelet packages. Finitely Supported wavelet bases for Sobolev spaces is researched. Steming from a pair of finitely supported refinale functions with multi-scaled dilation factor in space L 2(R 2) satsfying a very mild condition, we provide a novel method for designing wavelet bases, which is the generalization of univariate wavelets in Hilbert space. The definition of biorthogonal nonseparable bivariate wavelet wraps is provided and a procedure for designting them is proposed. The biorthogonality trait of binary wavelet wraps is studied by virtue of time-frequency analysis method and iterative method. Three biorthogonality formulas regarding these wavelet wraps are created. Moreover, it is shown how to get new Riesz bases of L 2(R 2) from the wavelet wraps.
Foundation item: The research is supported by Natural Scientific Foundation of Shaanxi Province (Grant No:2009J M1002), and by the Science Research Foundation of Education Department of Shaanxi Provincial Government (Grant No:11JK0468).
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© 2011 Springer-Verlag Berlin Heidelberg
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Tian, Y., Chen, Q. (2011). The Characteristics of Multiscaled Biorthogonal Binary Wavelet Wraps with Short Support and Applications in Computer Science. In: Lin, S., Huang, X. (eds) Advances in Computer Science, Environment, Ecoinformatics, and Education. CSEE 2011. Communications in Computer and Information Science, vol 217. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23339-5_11
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DOI: https://doi.org/10.1007/978-3-642-23339-5_11
Publisher Name: Springer, Berlin, Heidelberg
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