Multivariate symmetric refinable functions and function vectors

For any symmetry group ℋ, any appropriate matrix dilation (compatible with ℋ) and any appropriate symmetry center c we give an explicit method for the construction of ℋ-symmetric with respect to the center c refinable masks which have sum rule of an arbitrary order n. Moreover, we give a description of all these masks. For any symmetry group ℋ, any appropriate matrix dilation (compatible with ℋ) and any appropriate row of symmetry centers C we give two explicit methods for the construction of ℋ-symmetric with respect to the row of centers C refinable matrix masks which have sum rule of an arbitrary order n. A description of all such matrix masks is also presented.