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Fundam. Prikl. Mat., 2014, Volume 19, Issue 5, Pages 185–212 (Mi fpm1611)  

This article is cited in 5 scientific papers (total in 5 papers)

On the best linear approximation of holomorphic functions

Yu. A. Farkovab

a Russian State Geological Prospecting University
b Russian Academy of National Economy and Public Administration under the President of the Russian Federation

Abstract: Let $\Omega$ be an open subset of the complex plane $\mathbb C$ and let $E$ be a compact subset of $ \Omega$. The present survey is concerned with linear $n$-widths for the class $H^\infty(\Omega)$ in the space $C(E)$ and some problems on the best linear approximation of classes of Hardy–Sobolev-type in $L^p$-spaces. It is known that the partial sums of the Faber series give the classical method for approximation of functions $f\in H^\infty(\Omega)$ in the metric of $C(E)$ when $E$ is a bounded continuum with simply connected complement and $\Omega$ is a canonical neighborhood of $E$. Generalizations of the Faber series are defined for the case where $\Omega$ is a multiply connected domain or a disjoint union of several such domains, while $E$ can be split into a finite number of continua. The exact values of $n$-widths and asymptotic formulas for the $\varepsilon$-entropy of classes of holomorphic functions with bounded fractional derivatives in domains of tube type are presented. Also, some results about Faber's approximations in connection with their applications in numerical analysis are mentioned.

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English version:
Journal of Mathematical Sciences (New York), 2016, 218:5, 678–698

Bibliographic databases:

UDC: 517.538.5+517.551

Citation: Yu. A. Farkov, “On the best linear approximation of holomorphic functions”, Fundam. Prikl. Mat., 19:5 (2014), 185–212; J. Math. Sci., 218:5 (2016), 678–698

Citation in format AMSBIB
\by Yu.~A.~Farkov
\paper On the best linear approximation of holomorphic functions
\jour Fundam. Prikl. Mat.
\yr 2014
\vol 19
\issue 5
\pages 185--212
\jour J. Math. Sci.
\yr 2016
\vol 218
\issue 5
\pages 678--698

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    This publication is cited in the following articles:
    1. M. S. Saidusainov, “O nailuchshikh lineinykh metodakh priblizheniya nekotorykh klassov analiticheskikh funktsii v vesovom prostranstve Bergmana”, Chebyshevskii sb., 17:1 (2016), 240–253  mathnet  elib
    2. A. Yu. Trynin, “A criterion of convergence of Lagrange–Sturm–Liouville processes in terms of one-sided modulus of variation”, Russian Math. (Iz. VUZ), 62:8 (2018), 51–63  mathnet  crossref  isi
    3. A. Yu. Trynin, “Uniform convergence of Lagrange–Sturm–Liouville processes on one functional class”, Ufa Math. J., 10:2 (2018), 93–108  mathnet  crossref  isi
    4. A. Yu. Trynin, “Skhodimost protsessov Lagranzha–Shturma–Liuvillya dlya nepreryvnykh funktsii ogranichennoi variatsii”, Vladikavk. matem. zhurn., 20:4 (2018), 76–91  mathnet  crossref
    5. A. Yu. Trynin, “Sufficient condition for convergence of Lagrange–Sturm–Liouville processes in terms of one-sided modulus of continuity”, Comput. Math. Math. Phys., 58:11 (2018), 1716–1727  mathnet  crossref  crossref  isi  elib
  • Фундаментальная и прикладная математика
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