摘要
The construction and properties of interval multi-wavelets based on symmetric/anti-symmetric orthogonal multi-wavelets on L^2（R） with arbitrary supports and multiplicity 2 are introduced. The main contributions include that （1） we study the construction of general orthogonal interval multi-wavelets which preserve the polynomial-reproduction order, and obtain the parametric expressions of interval multi-wavelets; （2） we obtain the decomposition and reconstruction formulas of interval multi-wavelets; （3） we define the “balancing” concept of interval multi-wavelets for the first time and study the construction of orthogonal balancing multi-wavelets, which have been ignored in the past; （4） we study the necessary and sufficient conditions about the symmetry of interval multi-wavelets.
The construction and properties of interval multi-wavelets based on symmetric/anti-symmetric orthogonal multi-wavelets on L^2（R） with arbitrary supports and multiplicity 2 are introduced. The main contributions include that （1） we study the construction of general orthogonal interval multi-wavelets which preserve the polynomial-reproduction order, and obtain the parametric expressions of interval multi-wavelets; （2） we obtain the decomposition and reconstruction formulas of interval multi-wavelets; （3） we define the “balancing” concept of interval multi-wavelets for the first time and study the construction of orthogonal balancing multi-wavelets, which have been ignored in the past; （4） we study the necessary and sufficient conditions about the symmetry of interval multi-wavelets.
基金
This work was supported by the National Natural Science Foundation of China(Grant No．60375021)
the National Science Foundation of Hunan Province(Grant No．00JJY3096)
the Key Project of Hunan Provincial Education Department(Grant No．04A056)．
