Matematicheskii Sbornik
 RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Sb.: Year: Volume: Issue: Page: Find

 Mat. Sb., 2019, Volume 210, Number 10, Pages 3–16 (Mi msb8952)

An analogue of the two-constants theorem and optimal recovery of analytic functions

R. R. Akopyanab

a Ural Federal University named after the first President of Russia B.N. Yeltsin, Ekaterinburg, Russia
b N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia

Abstract: Several related extremal problems for analytic functions in a simply connected domain $G$ with rectifiable Jordan boundary $\Gamma$ are treated. The sharp inequality
$$|f(z)|\le\mathscr C^{r,q}(z;\gamma_0,\varphi_0;\gamma_1,\varphi_1)\|f\|^\alpha_{L^q_{\varphi_1}(\gamma_1)}\|f\|^{1-\alpha}_{L^r_{\varphi_0}(\gamma_0)}$$
is established between a value of an analytic function in the domain and the weighted integral norms of the restrictions of its boundary values to two measurable subsets $\gamma_1$ and $\gamma_0=\Gamma\setminus\gamma_1$ of the boundary of the domain. It is an analogue of the F. and R. Nevanlinna two-constants theorem. The corresponding problems of optimal recovery of a function from its approximate boundary values on $\gamma_1$ and of the best approximation to the functional of analytic extension of a function from the part of the boundary $\gamma_1$ into the domain are solved.
Bibliography: 35 titles.

Keywords: analytic functions, F. and R. Nevanlinna two-constants theorem, optimal recovery of a functional, best approximation of an unbounded functional by bounded functionals, harmonic measure.

 Funding Agency Grant Number Russian Foundation for Basic Research 15-01-02705-à Ministry of Education and Science of the Russian Federation 02.A03.21.0006ÍØ-9356.2016.1 This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 15-01-02705-a), by the Russian Academic Excellence Project ‘5-100’ (grant no. 02.A03.21.0006) and by the programme of the President of the Russian Federation for state support of leading scientific schools (grant no. ÍØ-9356.2016.1).

DOI: https://doi.org/10.4213/sm8952

Full text: PDF file (666 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2019, 210:10, 1348–1360

Bibliographic databases:

UDC: 517.538.3+517.544
MSC: Primary 30C85, 65E05; Secondary 30H99

Citation: R. R. Akopyan, “An analogue of the two-constants theorem and optimal recovery of analytic functions”, Mat. Sb., 210:10 (2019), 3–16; Sb. Math., 210:10 (2019), 1348–1360

Citation in format AMSBIB
\Bibitem{Ako19} \by R.~R.~Akopyan \paper An analogue of the two-constants theorem and optimal recovery of analytic functions \jour Mat. Sb. \yr 2019 \vol 210 \issue 10 \pages 3--16 \mathnet{http://mi.mathnet.ru/msb8952} \crossref{https://doi.org/10.4213/sm8952} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=4017585} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2019SbMat.210.1348A} \elib{https://elibrary.ru/item.asp?id=43288508} \transl \jour Sb. Math. \yr 2019 \vol 210 \issue 10 \pages 1348--1360 \crossref{https://doi.org/10.1070/SM8952} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000510717100001} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85082440464} 

• http://mi.mathnet.ru/eng/msb8952
• https://doi.org/10.4213/sm8952
• http://mi.mathnet.ru/eng/msb/v210/i10/p3

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Akopyan R.R., “Optimal Recovery of a Derivative of An Analytic Function From Values of the Function Given With An Error on a Part of the Boundary. II”, Anal. Math.
2. V. V. Arestov, R. R. Akopyan, “Zadacha Stechkina o nailuchshem priblizhenii neogranichennogo operatora ogranichennymi i rodstvennye ei zadachi”, Tr. IMM UrO RAN, 26, no. 4, 2020, 7–31
3. R. R. Akopyan, “Analog teoremy Adamara i svyazannye ekstremalnye zadachi na klasse analiticheskikh funktsii”, Tr. IMM UrO RAN, 26, no. 4, 2020, 32–47
•  Number of views: This page: 345 References: 18 First page: 16