Conditions on 7c and / are given for the pointwise and uniform convergence to the Cauchy principal value integral rmm _1<A<1, j-i x~x of a sequence of integrals of piecewise linear approximations to f(x) or g\(x) = (f(x) — f(X))/(x — A). The important special case, k(x) = (1 a;)a(l + x)13, is considered in detail.

The classical least squares solutions in C[−1,1] in terms of linear combinations of ul-traspherical polynomials are extended in order to estimate power series on (−1,1). Approximate rates of uniform and pointwise convergence are obtained, which correspond to recent results of U. Luther and G. Mastroianni on Fourier projections with respect to Jacobi polynomials.

Two measure preserving dynamical systems are weakly disjoint if some pointwise convergence property is satisfied by ergodic averages on their direct product (a precise definition is given below). Disjointness implies weak disjointness. We start studying this new concept, both by stating some general properties and by giving various examples. The content of the article is summarized in the intro...

We study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. The analysis of the approximate control problems is carried out. The uniform convergence of discretized controls to optimal controls is proven under natural assumptions by taking piecewise constant controls. Finally, ...

In the present paper, we study a certain integral modification of the well known Baskakov operators with the weight function of Beta basis function. We establish pointwise convergence, an asymptotic formula an error estimation and an inverse result in simultaneous approximation for these new operators.

This paper presents explicitly a survey of uniformly integrable sequences of random variables. We also study extensively several cases and conditions required for uniform integrability, with the establishment of some new conditions needed for the generalization of the earlier results obtained by many scholars and researchers, noting the links between uniform integrability and pointwise converge...

This paper presents a new, penetrating approach to Young measure convergence in an abstract, measure theoretical setting. It was started in [12, 13, 14] and given its definitive shape in [18, 22]. This approach is based on K-convergence, a device by which narrow convergence on P(R) can be systematically transferred to Young measure convergence. Here P(R) stands for the set of all probability me...

In this paper, two theorems are proved, one for existence of the operator L (f ; x, y, λ) and the others for its pointwise convergence to f (x 0 , y 0) , as (x, y, λ) tends to (x 0 , y 0 , λ 0). In contrast to previous works, the kernel function is radial.

The Bohl algebra B is the ring of linear combinations of functions te on the real line, where k is any nonnegative integer, and λ is any complex number, with pointwise operations. We show that the Bass stable rank and the topological stable rank of B (where we use the topology of uniform convergence) are infinite.