Geodesic
Approximation by linear fractional transformations of simple partial fractions and their differences
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2018), pp. 29-40

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We study applications of a property of simple partial fractions such that a difference $f-\rho$, where $\rho$ is a simple partial fraction of order at most $n$, under linear-fractional transformations becomes again a difference of certain function and certain simple partial fraction of order at most $n$ with quadratic weight. We prove a theorem of uniqueness of interpolating simple partial fraction, generalizing known results, and obtain estimates of best uniform approximation of certain functions on real semi-axis $\mathbb{R}^+$. For the first time, for continuous functions of rather common type we obtain estimates of best approximation by differences of simple partial fractions on $\mathbb{R}^+$, and for odd functions on all axis $\mathbb{R}$.
Keywords: simple partial fraction, linear-fractional transformation, best approximation, estimate, quadratic weight, differences of simple partial fractions.
Mots-clés : interpolation, semi-axis 
@article{IVM_2018_3_a3,
     author = {M. A. Komarov},
     title = {Approximation by linear fractional transformations of simple partial fractions and their differences},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {29--40},
     publisher = {mathdoc},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_3_a3/}
}
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M. A. Komarov. Approximation by linear fractional transformations of simple partial fractions and their differences. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2018), pp. 29-40. http://geodesic.mathdoc.fr/item/IVM_2018_3_a3/