A new class of multi-wavelet bases: V-system |
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| Authors: | Chao Huang Li Hua Yang Dong Xu Qi |
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| Affiliation: | (1) College of Mathematics and Computational Science, Shenzhen University, Shenzhen, 518060, P. R. China;(2) School of Mathematics and Computational Science, Sun Yat-sen University, Guangdong Province Key Laboratory of Computational Science, Guangzhou, 510275, P. R. China;(3) Faculty of Information Technology, Macau University of Science and Technology, Macau, P. R. China |
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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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| Keywords: | Multi-wavelets V-system complete orthogonal system |
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