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This paper is devoted to the study of the dimension functions of (multi)wavelets, which was introduced and investigated by P. Auscher in 1995 (J. Geom. Anal. 5, 181-236). Our main result provides a characterization of functions which are dimension functions of a (multi)wavelet. As a corollary, we obtain that for every function D that is the dimension function of a (multi)wavelet, there is a minimally supported frequency (multi)wavelet whose dimension function is D. In addition, we show that if a dimension function of a wavelet not associated with a multiresolution analysis (MRA) attains the value K, then it attains all integer values from 0 to K. Moreover, we prove that every expansive matrix which preserves Z N admits an MRA structure with an analytic (multi)wavelet.

The finite section method is a classical scheme to approximate the solution of an infinite system of linear equations. Based on an axiomatic framework we present a convergence analysis of the finite section method for unstructured matrices on weighted p -spaces. In particular, the stability of the finite section method on 2 implies its stability on weighted p -spaces. Our approach uses recent results from the theory of Banach algebras of matrices with off-diagonal decay. Furthermore, we demonstrate that Banach algebra theory provides a natural framework for deriving a finite section method that is applicable to large classes of unstructured non-hermitian matrices as well as to least squares problems.Mathematics Subject Classification (2010). 65J10, 47L80.

We extend the notion of the spectral function of shift-invariant spaces introduced by the authors in [BRz] to the case of general lattices. The main feature is that the spectral function is not dependent on the choice of the underlying lattice with respect to which a space is shift-invariant. We also show that in general the spectral function is not additive on the orthogonal infinite sums of SI spaces with varying lattices. 2000 Mathematics Subject Classification. 42C40.

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