This paper focuses on a method to construct wavelet Riesz bases with homogeneous boundary condition and use them kind of second-order elliptic equation. First, we the splines interval [0,1] consider their approximation properties. Then define illustrate numbers stiffness matrices are small bounded. Finally, several numerical examples show that our approach performs efficiently.

A dual frames multiplier is an operator consisting of analysis, multiplication and synthesis processes, where the analysis are made by two in a Hilbert space, respectively. In this paper we investigate spectra some multipliers giving, particular, conditions to be at most countable. The contribution extends results available literature about Bessel with symbol decaying zero Riesz bases.

In this paper we rst review the construction of stable Riesz bases for nite element spaces with respect to Sobolev norms. Then, we construct optimal order multilevel preconditioners for the matrices in the normal form of the equations arising in the nite element discretization of non{symmetric second order elliptic equations. The optimality of the AMLI methods is proven under H 2 {regularity as...

The efficient solution of operator equations using wavelets requires that they generate a Riesz basis for the underlying Sobolev space, and that they have cancellation properties of a sufficiently high order. Suitable biorthogonal wavelets were constructed on reference domains as the n-cube, which bases have been used, via a domain decomposition approach, as building blocks to construct biortho...

Let μ be a Borel probability measure with compact support. We consider exponential type orthonormal bases, Riesz bases and frames in L2(μ). We show that if L2(μ) admits an exponential frame, then μ must be of pure type. We also classify various μ that admits either kind of exponential bases, in particular, the discrete measures and their connection with integer tiles. By using this and convolut...

We show that every frame for a Hilbert space H can be written as a (multiple of a) sum of three orthonormal bases for H. We next show that this result is best possible by including a result of N.J. Kalton: A frame can be represented as a linear combination of two orthonormal bases if and only if it is a Riesz basis. We further show that every frame can be written as a (multiple of a) sum of two...