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The Features of Poly-scaled Non-orthogonal Bivariate Wavelet Packages and Applications in Finance Science

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Advances in Future Computer and Control Systems

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 159))

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Abstract

In this paper, a sort of bivariate wavelet packages with poly-scale are introduced, which are generalizations of univariant wavelet packets. Finitely Supported wavelet bases for Sobolev spaces is researched. Steming from a pair of finitely supported refinale functions with poly-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 erected. Moreover, it is shown how to get new Riesz bases of L 2(R 2) from the wavelet wraps.

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Author information

Authors and Affiliations

  1. Office of Financial Affairs, Henan Quality Polytechnic, Pingdingshan, 467000, P.R. China

    Yonggan Li

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  1. Yonggan Li
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Correspondence to Yonggan Li .

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Editors and Affiliations

  1. Researcher Association, Wuhan Section, International Science & Education, Special No.1, Jiangxia Road of Wuhan, Wuhan, China, People's Republic

    David Jin

  2. Researcher Association, Guangzhou Section, International Science & Education, Jinheng Road, Jinbi Garden 85-1102 144, Guang Zhou, China, People's Republic

    Sally Lin

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Li, Y. (2012). The Features of Poly-scaled Non-orthogonal Bivariate Wavelet Packages and Applications in Finance Science. In: Jin, D., Lin, S. (eds) Advances in Future Computer and Control Systems. Advances in Intelligent and Soft Computing, vol 159. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29387-0_21

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  • DOI: https://doi.org/10.1007/978-3-642-29387-0_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29386-3

  • Online ISBN: 978-3-642-29387-0

  • eBook Packages: EngineeringEngineering (R0)

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