Most of the research work on wavelet analysis so far has been concentrated on wavelets on uniform meshes in Euclidean spaces. We are interested in wavelet bases for function spaces on bounded domains with possibly nonuniform or irregular meshes. For this purpose, we introduce the projection method for construction of wavelet bases. Let (Vn)n=0,1,2,... be a family of closed subspaces of a Hilber...

In this article we propose a method to easily generate infinite multi-index positive definite self-adjoint matrices as well as Riesz bases in suitable subspaces of L2(Rd). The method is then applied to obtain some classes of multi-index Toeplitz matrices which are bounded and strictly positive on 2(Zd). The condition number of some of these matrices is also computed.

We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions, one being affinely dependent on the eigen-parameter. We give sufficient conditions under which a basis of each root subspace for this Sturm-Liouville problem can be selected so that the union of all these bases constitutes a Riesz basis of a corresponding weighted Hilbert space.

Orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide. We show here that under fairly general conditions, exact reconstruction schemes with synthesis filters different from the analysis filters give rise: to two dual Riesz bases of compactly supported wavelets. We give necessary ...

A sequence of vectors {f1, f2, f3, . . . } in a separable Hilbert space H is said to be a Schauder basis for H if every element f ∈ H has a unique norm-convergent expansion f = ∑ cnfn. If, in addition, there exist positive constants A and B such that A ∑ |cn| ≤ ∥∥∥∑ cnfn∥∥∥2 ≤ B∑ |cn|, then we call {f1, f2, f3, . . . } a Riesz basis. In the first half of this paper, we show that every Schauder ...

In this paper we extend the Balian-Low type theorems to Riesz bases for systems of many signals. We present the construction of coherent frames and we give su cient conditions for these frames to have coherentduals. Under these conditions we prove some nonlocalization theorems.