Approximation by Simplest Fractions

Pleiades Publishing Ltd - 2001
V. I. Danchenko1, D. Ya. Danchenko1
1Vladimir State University, Russia

Tóm tắt

In this paper, a number of problems concerning the uniform approximation of complex-valued continuous functions $$f\left( z \right)$$ on compact subsets of the complex plane by simplest fractions of the form $$\Theta _n \left( z \right) = \sum\nolimits_{j = 1}^n {{1 \mathord{\left/ {\vphantom {1 {\left( {z - z_j } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {z - z_j } \right)}}}$$ are considered. In particular, it is shown that the best approximation of a function $$f$$ by the fractions $$\Theta _n$$ is of the same order of vanishing as the best approximations by polynomials of degree $$ \leqslant n$$ .

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Tài liệu tham khảo

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