A sampling theorem for shift-invariant subspace generated by several scaling functions in L/sup 2/(R)

We construct the kernel of orthogonal projection in a shift-invariant subspace S(/spl sigma//sub 1/, /spl sigma//sub 2/, ..., /spl sigma//sub m/) generated by several scaling functions, and obtain the sampling theorem; by using the kernel of the orthogonal projection, we get the dual bases of the interpolation basis functions. We extend the results in the space generated by one scaling function to a more general space. In addition, these results have a more practical value.