Rate of convergence of beta operators of second kind for functions with derivatives of bounded variation.
It is shown that the Kolmogorov distance between the expected spectral distribution function of an n × n matrix from the Deformed Gaussian Ensemble and the distribution function of the semi-circle law is of order O(n −2/3+v ).
In this paper we establish an estimation for the rate of pointwise convergence of the Chlodovsky-Kantorovich polynomials for functions f locally integrable on the interval [0,∞). In particular, corresponding estimation for functions f measurable and locally bounded on [0,∞) is presented, too.
Let ⨍ be an analytic function on a compact subset K of the complex plane ℂ, and let denote the rational function of degree n with poles at the points and interpolating ⨍ at the points . We investigate how these points should be chosen to guarantee the convergence of to ⨍ as n → ∞ for all functions ⨍ analytic on K. When K has no “holes” (see [8] and [3]), it is possible to choose the poles without limit points on K. In this paper we study the case of general compact sets K, when such a separation...