Multiwavelets in the generalized Sobolev space H_W~ω(R~n)

摘要

A class of r-regular multiwavelets is introduced with appropriate notation and definitions in H_W~ω(R~n). The oscillation properity of the orthonormal system is obtained. A multiresolution analysis for multiwavelets is defined in H_W~ω(R~n). Orfhonormality conditions for multiscaling functions and multiwavelets are obtained. A multiwavelet expansion formula of Riesz potentials is given.