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A new class of multi-wavelet bases: V-system

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Abstract

The V-system is a complete orthogonal system of functions defined on the interval [0, 1], generated by finite Legendre polynomials and the dilation and translation of a function generator, which consists of a finite number of continuous and discontinuous functions. The V-system has interesting properties, such as orthogonality, symmetry, completeness and short compact support. It is shown in this paper that the V-system is essentially a special multi-wavelet basis. As a result, some basic properties of the V-system are established through the well-developed theory of multi-wavelets. From this point of view, more other V-systems are constructed.

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Authors and Affiliations

  1. College of Mathematics and Computational Science, Shenzhen University, Shenzhen, 518060, P. R. China

    Chao Huang

  2. School of Mathematics and Computational Science, Sun Yat-sen University, Guangdong Province Key Laboratory of Computational Science, Guangzhou, 510275, P. R. China

    Li Hua Yang

  3. Faculty of Information Technology, Macau University of Science and Technology, Macau, P. R. China

    Dong Xu Qi

Authors
  1. Chao Huang
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  2. Li Hua Yang
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  3. Dong Xu Qi
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Correspondence to Li Hua Yang.

Additional information

Supported by National Natural Science Foundation of China (Grant Nos. 11071261, 60873088 and 10911120394)

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Huang, C., Yang, L.H. & Qi, D.X. A new class of multi-wavelet bases: V-system. Acta. Math. Sin.-English Ser. 28, 105–120 (2012). https://doi.org/10.1007/s10114-012-9424-8

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  • DOI: https://doi.org/10.1007/s10114-012-9424-8

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