A study of orthonormal multi-wavelets on the interval

Abstract

The construction and properties of interval multi-wavelets based on orthonormal multi-wavelets on L ²(R) with arbitrary supports and multiplicity r are introduced. The interval multi-wavelets, which can preserve the polynomial reproduction order of corresponding multi-wavelets, are constructed and the decomposition and reconstruction formulas for interval multi-wavelet are obtained. We propose the “balancing” concept of the interval multi-wavelets and study the construction of orthogonal balancing multi-wavelets, which have been ignored in the past. We also study the symmetry of interval multi-wavelets and obtain necessary and sufficient conditions of it.

Keywords:

• Multi-wavelets
• Balancing
• Symmetry
• Orthogonality
• Accuracy order

Acknowledgements

This work was supported by the National Natural Science Foundation of China (60375021), by the Scientific Research Foundation for ROCS, SEM, by the Natural Science Foundation of Hunan province of China (05JJ10011), and by the Key Foundation of Department of Education of Hunan province of China (04A056).