Let μ be a measure with compact support, with orthonormal polynomials {pn}, and associated reproducing kernels {Kn}. We show that bulk universality holds in measure in {ξ : μ (ξ) > 0}. More precisely, given ε, r > 0, the linear Lebesgue measure of the set of ξ with μ (ξ) > 0 and for which

Let be a compactly supported positive measure on the real line, with associated orthogonal polynomials fpng. Without any global restrictions such as regularity, we discuss convergence in measure for (i) ratio asymptotics for Christo¤el functions; (ii) the Nevai operators (aka the Nevai condition); (iii) universality limits in the bulk. We also establish convergence a.e. for su¢ cently sparse su...

In this chapter the use of compactly-supported radial basis functions for surface reconstruction is described. To solve the problem of reconstruction or volume data generation specially designed software is employed. Time performance of the algorithm is investigated. Thanks to the efficient octree algorithm used in this study, the resulting matrix is a band diagonal matrix that reduces computat...

We propose a shift-invariant multiresolution representation of signals or images using dilations and translations of the autocorrelation functions of compactly supported wavelets. Although these functions do not form an orthonormal basis, their properties make them useful for signal and image analysis. Unlike wavelet-based orthonormal representations, our representation has 1) symmetric analyzi...

In this paper, we construct pairs of compactly supported dual wavelet frames for general dilations. We obtain smooth wavelets with small supports by convolution. Our approach leads to wavelets that have a high number of vanishing moments. Moreover, the corresponding refinable function is interpolating. The wavelets for the quincunx dilation matrix in our examples additionally have very high sym...

We give a formula for the duals of the masks associated with trivariate box spline functions. We show how to construct trivariate nonseparable compactly supported biorthogonal wavelets associated with box spline functions. The biorthogonal wavelets may have arbitrarily high regularities.

In this paper we construct Powell–Sabin spline multiwavelets on the hexagonal lattice in a shift-invariant setting. This allows us to use Fourier techniques to study the range of the smoothness parameter s for which the wavelet basis is a Riesz basis in the Sobolev space H(R), and we find that 0.431898 < s < 5/2. For those s, discretizations of H -elliptic problems with respect to the wavelet b...

In this paper we consider landmark-based image registration using radial basis function interpolation schemes. More precisely, we analyze some landmark-based image transformations using compactly supported radial basis functions such as Wendland’s, Wu’s, and Gneiting’s functions. Comparisons of interpolation techniques are performed and numerical experiments show differences in accuracy and smo...

In applications that involve interactive curve and surface modeling, the intuitive manipulation of shapes is crucial. For instance, user interaction is facilitated if a geometrical object can be manipulated through control points that interpolate the shape itself. Additionally, models for shape representation often need to provide local shape control and they need to be able to reproduce common...

In this paper, we develop a fast algorithm for a smoothing spline estimator in multivariate regression. To accomplish this, we employ general concepts associated with roughness penalty methods in conjunction with the theory of radial basis functions and reproducing kernel Hilbert spaces. It is shown that through the use of compactly supported radial basis functions it becomes possible to recove...