Abstract:
This article contains a proof of the following fact: for any bounded function f(z)f(z), |z|=1|z|=1, of the first Baire class such that ∫|z|=1f(z)zndz=0∫|z|=1f(z)zndz=0 for n=0,1,…n=0,1,…, there exists a uniformly bounded sequence of polynomials on |z|=1|z|=1 converging pointwise to f(z)f(z).
Bibliography: 2 titles.
Citation:
S. V. Kolesnikov, “On a theorem of M. V. Keldysh concerning pointwise convergence of a sequence of polynomials”, Math. USSR-Sb., 52:2 (1985), 553–555
\Bibitem{Kol84}
\by S.~V.~Kolesnikov
\paper On a~theorem of M.\,V.~Keldysh concerning pointwise convergence of a~sequence of polynomials
\jour Math. USSR-Sb.
\yr 1985
\vol 52
\issue 2
\pages 553--555
\mathnet{http://mi.mathnet.ru/eng/sm2067}
\crossref{https://doi.org/10.1070/SM1985v052n02ABEH002905}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=754477}
\zmath{https://zbmath.org/?q=an:0578.30031}
Linking options:
https://www.mathnet.ru/eng/sm2067
https://doi.org/10.1070/SM1985v052n02ABEH002905
https://www.mathnet.ru/eng/sm/v166/i4/p568
This publication is cited in the following 6 articles:
M. Ya. Mazalov, “Criterion of uniform approximability by harmonic functions on compact sets in R3”, Proc. Steklov Inst. Math., 279 (2012), 110–154
Danielyan A.A., “The Peak-Interpolation Theorem of Bishop”, Complex Analysis and Dynamical Systems IV, Pt 1: Function Theory and Optimization, Contemporary Mathematics, 553, eds. Agranovsky M., BenArtzi M., Galloway G., Karp L., Reich S., Shoikhet D., Weinstein G., Zalcman L., Amer Mathematical Soc, 2011, 27–30
Danielyan A.A., “On a Polynomial Approximation Problem”, J. Approx. Theory, 162:4 (2010), 717–722
M. Ya. Mazalov, “A criterion for uniform approximability on arbitrary compact sets for solutions of elliptic equations”, Sb. Math., 199:1 (2008), 13–44
Danielyan A., Saff E., “An Extension of E. Bishop's Localization Theorem”, J. Approx. Theory, 109:1 (2001), 148–156
A. A. Danielyan, “On a problem of M. A. Lavrent'ev concerning the representability of functions by series of polynomials in the complex domain”, Izv. Math., 63:2 (1999), 245–254
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