Matematicheskie Zametki
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. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 2020, Volume 108, Issue 6, Pages 803–822 (Mi mz12598)  

Estimates of the Values of $n$-Widths of Classes of Analytic Functions in the Weight Spaces $H_{2,\gamma}(D)$

S. B. Vakarchuk

Alfred Nobel University Dnepropetrovsk

Abstract: In a simply connected bounded domain $D\subset\mathbb C$ with rectifiable Jordan boundary $\partial D$, we study the classes $H_{2,\gamma}(D;\Omega_k,\Phi)$, $k\in\mathbb N$, consisting of analytic functions $f\in H_{2,\gamma}(D)$ in $D$ each of which, for any $t\in(0,1)$, satisfies the condition $\Omega_k(f,t)\le\Phi(t)$. Here $\Omega_k(f)$ is the generalized modulus of continuity of $k$th order in $H_{2,\gamma}(D)$ and $\Phi$ is a majorant. For these classes, we find upper and lower bounds for various $n$-widths, as well as upper bounds for the moduli of Fourier coefficients. We obtain a constraint on the majorant $\Phi$ under which the exact values of these extremal characteristics can be calculated. In the case of the unit disk, similar results are obtained for classes of analytic functions whose definitions include the Hadamard compositions $\mathscr D(\mathscr B_m,f)$ in addition to $\Omega_k(f)$ and $\Phi$. Concrete realizations of some obtained exact results are presented.

Keywords: weight function, orthogonal system of polynomials, generalized modulus of continuity, majorant, Fourier series, Fourier coefficient, Hadamard composition, $n$-width.

DOI: https://doi.org/10.4213/mzm12598

Full text: PDF file (657 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Mathematical Notes, 2020, 108:6, 775–790

Bibliographic databases:

UDC: 517.5
Received: 30.10.2019
Revised: 03.09.2020

Citation: S. B. Vakarchuk, “Estimates of the Values of $n$-Widths of Classes of Analytic Functions in the Weight Spaces $H_{2,\gamma}(D)$”, Mat. Zametki, 108:6 (2020), 803–822; Math. Notes, 108:6 (2020), 775–790

Citation in format AMSBIB
\Bibitem{Vak20}
\by S.~B.~Vakarchuk
\paper Estimates of the Values of $n$-Widths of Classes of Analytic Functions in the Weight Spaces $H_{2,\gamma}(D)$
\jour Mat. Zametki
\yr 2020
\vol 108
\issue 6
\pages 803--822
\mathnet{http://mi.mathnet.ru/mz12598}
\crossref{https://doi.org/10.4213/mzm12598}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=4181042}
\elib{https://elibrary.ru/item.asp?id=45084322}
\transl
\jour Math. Notes
\yr 2020
\vol 108
\issue 6
\pages 775--790
\crossref{https://doi.org/10.1134/S0001434620110218}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000599343700020}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85097531009}


Linking options:
  • http://mi.mathnet.ru/eng/mz12598
  • https://doi.org/10.4213/mzm12598
  • http://mi.mathnet.ru/eng/mz/v108/i6/p803

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Математические заметки Mathematical Notes
    Number of views:
    This page:127
    References:20
    First page:24

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021