Let μ be a measure from Szegő class on the unit circle T and let {fn} family of Schur functions generated by μ. In this paper, we prove version classical Szegő's formula, which controls oscillation fn for all n⩾0. Then, focus an analog Lusin's conjecture polynomials {φn} orthogonal with respect to that pointwise convergence {|φn|} almost everywhere is equivalent certain condition zeroes φn.

We consider a modiication of moment functionals for the Hahn classical polynomials of a discrete variable by adding two mass points at the ends of the interval, i.e., in x = 0 and x = N 1. We obtain the resulting orthogonal polynomials and identify them as hypergeometric functions. The corresponding three term recurrence relation and tridiagonal matrices are also studied. x1 Introduction. The s...

in this paper, we introduce hybrid of block-pulse functions and bernstein polynomials and derive operational matrices of integration, dual, differentiation, product and delay of these hybrid functions by a general procedure that can be used for other polynomials or orthogonal functions. then, we utilize them to solvedelay differential equations and time-delay system. the method is based upon ex...

Monte-Carlo computations often yield numerical answers of limited accuracy, and are therefore employed as a last resort. It has been found, however, that some of the limitations of Monte-Carlo methods can be overcome through a judicious use of orthogonal expansions. When a numerical answer is obtained as the expected value of an estimator, expansion of that estimator in a series of orthogonal f...

The aim of this paper is to introduce two new extensions of the Jacobi and Laguerre polynomials as the eigenfunctions of two non-classical Sturm-Liouville problems. We prove some important properties of these operators such as: These sets of functions are orthogonal with respect to a positive de nite inner product de ned over the compact intervals [-1, 1] and [0,1), respectively and also th...

The system of Gegenbauer or ultraspherical polynomials $Cn (x);n50,1,.. .% is a classical family of polynomials orthogonal with respect to the weight function vl(x)5(12x ) on the support interval @21,11# . Integral functionals of Gegenbauer polynomials with integrand f (x)@Cn (x)#vl(x), where f (x) is an arbitrary function which does not depend on n or l, are considered in this paper. First, a ...