On Stability of Scaling Vectors

The paper generalizes Lawton s criteria for scaling vectors by means of Kronecker products Necessary and su cient conditions for the stability orthonormality of scaling vectors are provided in terms of their two scale symbols The paper is based on the results of Shen x Introduction Usually the construction of multiwavelets is based on a multiresolution anal ysis MRA with higher multiplicity In order to generate the MRA a re n able function vector r T r IN r is needed such that B f l l ZZ r g forms an L stable basis of its span Moreover the components of are often desired to be compactly supported regular and symmetric or antisymmetric such that multiwavelets with similar properties can be derived The compactly supported scaling vector can be considered as a solution vector of a matrix re nement equation