Izv. Vyssh. Uchebn. Zaved. Mat., 2018, Number 12, Pages 9–49
Extremal and approximative properties of simple partial fractions
V. I. Danchenko, M. A. Komarov, P. V. Chunaev
Vladimir State University named after Alexander and Nikolai Stoletovs,
87 Gor’kogo str., Vladimir, 600000 Russia
In approximation theory, logarithmic derivatives of complex polynomials are called simple partial fractions (SPF) as suggested by E.P. Dolzhenko. Many solved and unsolved extremal problems related to SPF are traced back to works of G. Boole, A.J. Macintyre, W.H.J. Fuchs, J.M. Marstrand, E.A. Gorin, A.A. Gonchar, E.P. Dolzhenko. At present, many authors systematically develop methods for approximation and interpolation by SPF and several their modifications. Simultaneously, related problems, being of independent interest, arise for SPF: inequalities of different metrics, estimation of derivatives, separation of singularities, etc.
We systematize some of these problems which are known to us in Introduction of this survey. In the main part, we formulate principal results and outline methods to prove them if possible.
Gorin–Gelfond problems, simple partial fractions, amplitude and frequency operators, alternance, best approximations, rational functions, approximation, interpolation, extrapolation.
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V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Extremal and approximative properties of simple partial fractions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 12, 9–49
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\by V.~I.~Danchenko, M.~A.~Komarov, P.~V.~Chunaev
\paper Extremal and approximative properties of simple partial fractions
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
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