相关论文: Krein's entire functions and the Bernstein approxi…
We give direct and inverse theorems for the weighted approximation of functions with endpoint singularities by combinations of Bernstein operators.
The Bernstein approximation problem is to determine whether or not the space of all polynomials is dense in a given weighted $C_0$-space on the real line. A theorem of L. de Branges characterizes non--density by existence of an entire…
We give direct and inverse theorems for the weighted approximation of functions with inner singularities by combinations of Bernstein polynomials.
We extend some results of M.G. Krein to the class of entire functions which can be represented as ratios of discrete Cauchy transforms in the plane. As an application we obtain new versions of de Branges' Ordering Theorem for nearly…
We generalize the classical Bernstein theorem concerning the constructive description of classes of functions uniformly continuous on the real line. The approximation of continuous bounded functions by entire functions of exponential type…
A new type of combinations of Bernstein operators is given in [1]. Here, we introduce another one, which can be used to approximate the functions with singularities. The direct and inverse results of the weighted approximation of this new…
Extencion of Krein's special method for solving of integral equation to that method for solving of systems of integral equations is established. Generalizations of formulae for solution of integral equations are obtained. The result…
We introduce a new type of Bernstein operators, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type of combinations are given.
Three approximation problems in Krein spaces are studied, namely the indefinite weighted least squares problem and the related problems of indefinite abstract splines and smoothing. In every case, we analyze if the problem has a solution…
We investigate subclasses of generalized Bernstein functions related to complete Bernstein and Thorin-Bernstein functions. Representations in terms of incomplete beta and gamma as well as hypergeometric functions are presented. Several…
Final representation of all those measures $\mu$ for which algebraic polynomials are dense in $L_p(R, d\mu)$ is found. The weighted analogue of the Weierstrass polynomial approximation theorem and a new version of the M. Krein's theorem…
We establish sharp inequalities involving the incomplete Beta and Gamma functions. These inequalities arise in the approximation of generalized Bernstein functions by higher order Thorin-Bernstein functions. Furthermore, new properties of a…
We introduce another new type of combinations of Bernstein operators in this paper, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type…
The aim of this paper is to give an effective version of the Strong Artin Approximation Theorem for binomial equations. First we give an effective version of the Greenberg Approximation Theorem for polynomial equations, then using the…
We consider the pointwise weighted approximation by Bernstein operators with inner singularities. The related weight functions are weights $\bar{w}(x)=|x-\xi|^\alpha(0<\xi<1,\ \alpha>0).$ In this paper we give direct and inverse results of…
A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…
This work presents a contemporary treatment of Krein's entire operators with deficiency indices $(1,1)$ and de Branges' Hilbert spaces of entire functions. Each of these theories played a central role in the research of both renown…
We present analytical approximations for the real Kelvin function ber(x) and the imaginary Kelvin function bei(x), using the two-point quasifractional approximation procedure. We have applied these approximations to the calculation of the…
Cartwright-type and Bernstein-type theorems, previously known only for functions of exponential type in $\C^n$, are extended to the case of functions of arbitrary order in a cone.
The paper presents new and known results on estimates of important linear and nonlinear approximation characteristics of generalized Wiener classes of functions of several variables in different metrics.