This article is cited in 17 papers

Biorthogonal systems of rational functions and best approximation of the Cauchy kernel on the real axis

M. M. Dzhrbashyan


Abstract: This paper is devoted to problems of the representation and best approximation of the Cauchy kernel on the whole real axis $-\infty<x<+\infty$. The method proposed here for the solution of such problems is based on the attraction of systems of rational functions with fixed poles which are orthogonal or biorthogonal on the whole axis.
Bibliography: 9 titles.

UDC: 517.53

MSC: Primary 41A20, 41A50; Secondary 42A56

Received: 14.01.1974

 English version: Mathematics of the USSR-Sbornik, 1974, 24:3, 409–433

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