Some equations relating multiwavelets and multiscaling functions

The local trace function introduced in [Dutkay, The local trace function of shift invariant spaces, J. Operat. Theory 52(2) (2004), 267-291] is used to derive equations that relate multiwavelets and multiscaling functions in the context of a generalized multiresolution analysis, without appealing to filters. A construction of normalized tight frame (NTF) wavelets is given. Particular instances of the construction include NTF and orthonormal wavelet sets.