As usual, we consider integral operators attached to compactly supported measures η on the group G, and exploit the intrinsic sense of such operators on any reasonable representation space for G, for example, Hilbert, Banach, Fréchet, and LF (strict colimits of Fréchet), or, generally,, quasi-complete, locally convex spaces. For a representation π, V of G, and a compactly-supported measure η, t...

In this paper we investigate the use of compactly supported RBF kernels for nonlinear function estimation with LS-SVMs. The choice of compact kernels recently proposed by Genton may lead to computational improvements and memory reduction. Examples however illustrate that compactly supported RBF kernels may lead to severe loss in generalization performance for some applications, e.g. in chaotic ...

Compactly supported Riesz wavelets are of interest in several applications such as image processing, computer graphics and numerical algorithms. In this paper, we shall investigate compactly supported MRA Riesz multiwavelet bases in L2(R). An algorithm is presented to derive Riesz multiwavelet bases from refinable function vectors. To illustrate our algorithm and results in this paper, we prese...

We begin by introducing some notation and definitions to get our investigation of compactly supported cohomolgy started. We then proceed to compute the compactly supported cohomology groups of simple spaces like ∗ = R, R and R. From these special cases, we will see how to generalize the computation to R. ereaer, we will prove the general version of the Poincaré Lemma, whi states H• c (M × R)...

Regularization with radial basis functions is an effective method in many machine learning applications. In recent years classes of radial basis functions with compact support have been proposed in the approximation theory literature and have become more and more popular due to their computational advantages. In this paper we study the statistical properties of the method of regularization with...

Linear independence of integer shifts of compactly supported functions plays an important role in approximation theory and wavelet analysis. In this note we provide a simple proof for two known characterizations of linear independence of integer shifts of a finite number of compactly supported distributions on R. By l(Z) we denote the space of all complex-valued sequences v = {v(k)}k∈Zd : Z → C...

In this paper, a compactly supported distribution which is linearly independent , and both m and n reenable for some integer pair (m; n) satisfying m r 6 = n s for all positive integers r and s, is shown to be essentially a B-spline. Combining the characterization of compactly supported distributions which are linearly independent, and both m and n reenable for some integer pair (m; n) satisfyi...