Biorthogonal multiple wavelets generated by vector refinement equation

【摘要】 <正>Biorthogonal multiple wavelets are generated from refinable function vectors by using the multiresolution analysis.In this paper we provide a general method for the construction of compactly supported biorthogonal multiple wavelets by refinable function vectors which are the solutions of vector refinement equations of the form （?）（x）=（?）a（α）（?）（Mx-α）,x∈R^s, where the vector of functions（?）=（（?）₁,...,（?）_r）^T is in（L₂（R^s））^r,a=:（a（α））_α∈Z^sis a finitely supported sequence of r×r matrices called the refinement mask,and M is an s×s integer matrix such that lim_n→∞M^-n=0.Our characterizations are in the general setting and the main results of this paper are the real extensions of some known results.更多还原

【Abstract】 Biorthogonal multiple wavelets are generated from refinable function vectors by using the multiresolution analysis.In this paper we provide a general method for the construction of compactly supported biorthogonal multiple wavelets by refinable function vectors which are the solutions of vector refinement equations of the form （?）（x）=（?）a（α）（?）（Mx-α）,x∈R^s, where the vector of functions（?）=（（?）₁,...,（?）_r）^T is in（L₂（R^s））^r,a=:（a（α））_α∈Z^sis a finitely supported sequence of r×r matrices called the refinement mask,and M is an s×s integer matrix such that lim_n→∞M^-n=0.Our characterizations are in the general setting and the main results of this paper are the real extensions of some known results.更多还原