Abstract. For orthogonal polynomials defined by compact Jacobi matrix with exponential decay of the coefficients, precise properties of orthogonality measure is determined. This allows showing uniform boundedness of partial sums of orthogonal expansions with respect to L∞ norm, which generalize analogous results obtained for little qLegendre, little q-Jacobi and little q-Laguerre polynomials, b...

Generalizing the case of an infinite discrete metric space finite diameter, we say that a (X,d) is Kuiper space, if group invertible elements its uniform Roe algebra norm-contractible. Various sufficient conditions on to be or not are obtained.

In this paper we consider a Dirichlet problem for singularly perturbed ordinary differential equations with convection terms and a small perturbation parameter ε. To solve the problem numerically we use an ε-uniformly convergent difference scheme (on special piecewise-uniform meshes) and a decomposition of this scheme based on a Schwarz technique with overlapping subdomains. The step-size of su...

Compressed sensing (CS) methods can be used to reconstruct MRI signals from highly undersampled data [1]. Recent studies have shown that selecting gridded samples using a Poisson disk sampling pattern yields improved reconstructions over the traditional uniform random sampling of a Cartesian grid [2]. We extend this work by evaluating the effects of Poisson disk sampling of a continuous k-space...

The phase error, or the pollution effect in the finite element solution of wave propagation problems, is a well known phenomenon that must be confronted when solving problems in the high-frequency range. This paper presents a new method with no phase errors for onedimensional time-harmonic wave propagation problems. The method is constructed within the framework of the Discontinuous Petrov-Gale...

The phase error, or the pollution effect in the finite element solution of wave propagation problems, is a well known phenomenon that must be confronted when solving problems in the highfrequency range. This paper presents a new method with no phase errors for one-dimensional (1D) time-harmonic wave propagation problems using new ideas that hold promise for the multidimensional case. The method...

We derive a three-term recurrence relation for computing the polynomial of best approximation in the uniform norm to x−1 on a finite interval with positive endpoints. As application, we consider two-level methods for scalar elliptic partial differential equation (PDE), where the relaxation on the fine grid uses the aforementioned polynomial of best approximation. Based on a new smoothing proper...

We present a sharp uniform-in-bandwidth functional limit law for the increments of the Kaplan-Meier empirical process based upon right-censored random data. We apply this result to obtain limit laws for nonparametric kernel estimators of local functionals of lifetime densities, which are uniform with respect to the choices of bandwidth and kernel. These are established in the framework of conve...

We investigate a mean field approximation to the statistical mechanics of complex fields with dynamics governed by the nonlinear Schr6dinger equation. Such fields, whose Hamiltonian is unbounded below, may model plasmas, lasers, and other physical systems. Restricting ourselves to one-dimensional systems with periodic boundary conditions, we find in the mean field approximation a phase transiti...

The authors consider the generalized airfoil equation in some weighted Hölder–Zygmund spaces with uniform norms. Using a projection method based on the de la Vallée Poussin interpolation, they find an approximate polynomial solution which converges to the original solution like the best uniform weighted polynomial approximation. The proposed numerical procedure leads to solve a tridiagonal line...