Integer-translates of compactly supported univariate refinable functions φi , such as cardinal B-splines, have been used extensively in computational mathematics. Using certain appropriate direction vectors, the notion of (multivariate) box splines can be generalized to (non-tensor-product) compactly supported multivariate refinable functions from the φi ’s. The objective of this paper is to in...

in this paper, we study l1 -solutions of the following two-direction poly-scale refinement equationwe prove that the vector space of all l1 -solutions of the above equation is at most one-dimensional andconsists of compactly supported functions of constant sign. we also show that any- l1 solution of the aboveequation is either positive or negative on its support under a special assumption. with...

The paper is concerned with the introduction and study of multiresolution analysis based on the up function, which is an innnitely diierentiable function supported on 0 2]. Such analysis is, necessarily, nonstationary. It is shown that the approximation orders associated with the corresponding spaces are spectral, thus making the spaces attractive for the approximation of very smooth functions.

A small perturbation method is developed and deployed to the construction of frames with compactly supported elements of small shrinking supports for Besov and Triebel-Lizorkin spaces in the general setting of a doubling metric measure space in presence of a non-negative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. This allows, in particular, to dev...

We study spectral properties of convolution operators L and their perturbations H = L+ v(x) by compactly supported potentials. Results are applied to determine the front propagation of a population density governed by operator H with a compactly supported initial density provided that H has positive eigenvalues. If there is no positive spectrum, then the stabilization of the population density ...

Let A be a matrix with the absolute values of all eigenvalues strictly larger than one, and let Z 0 be a subset of Z such that n 2 Z 0 implies n + 1 2 Z 0. Denote the space of all compactly supported distributions by D 0 , and the usual convolution between two compactly supported distributions f and g by f g.

We study resonances associated to Schrödinger operators with compactly supported potentials on R, d ≥ 3, odd. We consider compactly supported potentials depending holomorphically on a parameter z ∈ C. For certain such families, for all z except those in a pluripolar set, the associated resonance-counting function has order of growth d.