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Rates of convergence of Chlodovsky-Kantorovich polynomials in classes of locally integrable functions

Paulina Pych-Taberska (2009)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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.

Rational interpolants with preassigned poles, theoretical aspects

Amiran Ambroladze, Hans Wallin (1999)

Studia Mathematica

Let ⨍ be an analytic function on a compact subset K of the complex plane ℂ, and let r n ( z ) denote the rational function of degree n with poles at the points b n i i = 1 n and interpolating ⨍ at the points a n i i = 0 n . We investigate how these points should be chosen to guarantee the convergence of r n 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 b n i i , n without limit points on K. In this paper we study the case of general compact sets K, when such a separation...

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