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CONSTRUCTION OF THE MULTI-WAVELETS ON SOME SMOOTH PLANE CURVES VIA LENGTH-PRESERVING PROJECTION

BAOQIN WANG

School of Mathematical Science, Xinjiang Normal University, Urumqi, Xinjiang 830054, P. R. China

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GANG WANG

School of Mathematical Science, Xinjiang Normal University, Urumqi, Xinjiang 830054, P. R. China

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, and

XIAOHUI ZHOU

School of Mathematical Science, Xinjiang Normal University, Urumqi, Xinjiang 830054, P. R. China

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https://doi.org/10.1142/S0219691314500052Cited by:4 (Source: Crossref)

Abstract

Based on the theory of the discrete multi-wavelets in the space L²(R), the theory of the discrete multi-wavelets in the space L²(C) is presented properly in this paper, where C denotes a smooth plane curve. Firstly, the length-preserving projection is constructed, and by the length-preserving projection, the multiplicity multi-resolution analysis in the space L²(C) is defined properly and we define the dilation operator and translation operator in the space L²(C). Then, the two-scale refinement equations of multi-scaling function and multi-wavelet in the space L²(C) is deduced by using length-preserving mapping, the orthogonality is discussed, and the decomposition and reconstruction algorithm is computed. Finally, the example is given.

Keywords:

AMSC: 42C40, 65T60

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