We give new formulae for analytic balayage of measures supported on subsets of Carathéodory compact sets in the complex plane, and consider a related problem of description of badly approximable functions in .
Nous donnons de nouvelles formules pour le balayage analytique des mesures supportées sur des sous-ensembles d'ensembles compacts de Carathéodory dans le plan complexe et considérons le problème connexe de la description des fonctions mal approximables dans .
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@article{CRMATH_2018__356_8_870_0,
author = {Abakumov, Evgeny and Fedorovskiy, Konstantin},
title = {Analytic balayage of measures, {Carath\'eodory} domains, and badly approximable functions in {\protect\emph{L}\protect\textsuperscript{\protect\emph{p}}}},
journal = {Comptes Rendus. Math\'ematique},
pages = {870--874},
publisher = {Elsevier},
volume = {356},
number = {8},
year = {2018},
doi = {10.1016/j.crma.2018.05.018},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.crma.2018.05.018/}
}
TY - JOUR AU - Abakumov, Evgeny AU - Fedorovskiy, Konstantin TI - Analytic balayage of measures, Carathéodory domains, and badly approximable functions in Lp JO - Comptes Rendus. Mathématique PY - 2018 SP - 870 EP - 874 VL - 356 IS - 8 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.crma.2018.05.018/ DO - 10.1016/j.crma.2018.05.018 LA - en ID - CRMATH_2018__356_8_870_0 ER -
%0 Journal Article %A Abakumov, Evgeny %A Fedorovskiy, Konstantin %T Analytic balayage of measures, Carathéodory domains, and badly approximable functions in Lp %J Comptes Rendus. Mathématique %D 2018 %P 870-874 %V 356 %N 8 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.crma.2018.05.018/ %R 10.1016/j.crma.2018.05.018 %G en %F CRMATH_2018__356_8_870_0
Abakumov, Evgeny; Fedorovskiy, Konstantin. Analytic balayage of measures, Carathéodory domains, and badly approximable functions in Lp. Comptes Rendus. Mathématique, Volume 356 (2018) no. 8, pp. 870-874. doi : 10.1016/j.crma.2018.05.018. https://www.numdam.org/articles/10.1016/j.crma.2018.05.018/
[1] Badly approximable unimodular functions in weighted spaces, Comput. Methods Funct. Theory, Volume 4 (2004) no. 2, pp. 315-326
[2] Density of certain polynomial modules, J. Approx. Theory, Volume 206 (2016), pp. 1-16
[3] Analytic approximation of matrix functions in , J. Approx. Theory, Volume 158 (2009), pp. 242-278
[4] Analytic approximation in and coinvariant subspaces of the Hardy space, J. Approx. Theory, Volume 174 (2013), pp. 113-120
[5] Conformal maps and uniform approximation by polyanalytic functions, Oper. Theory, Adv. Appl., Volume 158 (2005), pp. 109-130
[6] New conditions for uniform approximation by polyanalytic polynomials, Tr. Mat. Inst. Steklova, Volume 279 (2012), pp. 227-241 (translation in Proc. Steklov Inst. Math., 279, 2012, pp. 215-229)
[7] On uniform approximation by polyanalytic polynomials and the Dirichlet problem for bianalytic functions, Mat. Sb., Volume 193 (2002) no. 10, pp. 75-98 (in Russian); English translation in Sb. Math., 193, 9–10, 2002, pp. 1469-1492
[8] Moduli and arguments of analytic functions from subspaces in that are invariant under the backward shift operator, Sib. Mat. Zh., Volume 31 (1990) no. 6, pp. 64-79 (in Russian); English translation in Sib. Math. J., 31, 6, 1990, pp. 926-939
[9] Carathéodory sets and analytic balayage of measures, Sb. Math. (2018) | DOI
[10] Bounded Analytic Function, Academic Press, 1981
[11] On some extremal problems of the theory of analytic functions, Matematika, IV, Moskov. Univ. Uchen. Zap., vol. 148, Moscow State University, Moscow, 1951, pp. 133-143 English translation, Amer. Math. Soc. Transl. (2), vol. 32, 1963, American Mathematical Society, Providence, RI, USA, pp. 139-154
[12] F. and M. Riesz theorem, analytic balayage, and problems in rational approximation, Constr. Approx., Volume 4 (1988), pp. 341-356
[13] Best approximation in the mean be analytic and harmonic functions, Indiana Univ. Math. J., Volume 49 (2000) no. 4, pp. 1481-1513
[14] Extremal problems in , J. Aust. Math. Soc. A, Volume 52 (1992), pp. 103-110
[15] Boundary Properties of Analytic Functions, Hochschulbücher für Mathematik, Bd. 25, GITTL, Moscow, 1950 (German transl.: Randeigenschaften analytischer Funktionen, 1956, VEB Deutscher Verlag der Wissenschaften, Berlin)
[16] Real and Complex Analysis, McGraw-Hill Book Co., New York, 1987
[17] Best approximation by holomorphic functions. Application to the best polynomial approximation of classes of holomorphic functions, Ukr. Math. J., Volume 59 (2007) no. 8, pp. 1163-1183
[18] Interpolation and Approximation by Rational Functions in the Complex Domain, American Mathematical Society, Providence, RI, USA, 1960
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