Multivariate symmetric refinable functions and function vectors

Abstract

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