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






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


Mat. Sb., 1994, Volume 185, Number 10, Pages 145–160 (Mi msb935)  

This article is cited in 1 scientific paper (total in 1 paper)

Metric characteristics of exceptional sets arising in estimates of subharmonic functions

V. Ya. Èiderman

Moscow State University of Civil Engineering

Abstract: The classes $U_{\mathrm{reg}}$ of subharmonic functions $u(x)$, $x\in\mathbb R^m$, $m\geqslant2$, of finite proximate order are considered, which generalize the class of functions of the form $u(z)=\ln|f(z)|$, where $f(z)$ is an entire function of completely regular growth in the sense of Levin–Pfluger. Estimates are obtained for the exceptional sets $C$ for functions $u(x)\in U_{\mathrm{reg}}$ containing the centers and radii of the balls covering $C$. Coverings of various structures are studied. In particular, the following problem is solved: Under what conditions on a continuous increasing function $h(t)$, $t\geqslant0$, $h(0)=0$, can the set $C$ be covered by balls $B_j(x_j,r_j)=\{x\in\mathbb R^m:|x-x_j|<r_j\}$ such that $\sum_{|x_j|<R}h(r_j/R)=o(1)$ as $R\to\infty$. In an approach proposed by V. S. Azarin these problems reduce to studying the connection between convergence in the topology of the space $\mathscr D'$ of generalized functions and convergence outside the exceptional sets.

Full text: PDF file (1526 kB)
References: PDF file   HTML file

English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1995, 83:1, 283–296

Bibliographic databases:

UDC: 517.535
MSC: Primary 30D15, 31B05; Secondary 31A15, 30C85
Received: 28.12.1992 and 08.12.1993

Citation: V. Ya. Èiderman, “Metric characteristics of exceptional sets arising in estimates of subharmonic functions”, Mat. Sb., 185:10 (1994), 145–160; Russian Acad. Sci. Sb. Math., 83:1 (1995), 283–296

Citation in format AMSBIB
\Bibitem{Eid94}
\by V.~Ya.~\`Eiderman
\paper Metric characteristics of exceptional sets arising in estimates of subharmonic functions
\jour Mat. Sb.
\yr 1994
\vol 185
\issue 10
\pages 145--160
\mathnet{http://mi.mathnet.ru/msb935}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1309185}
\zmath{https://zbmath.org/?q=an:0846.31004}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 83
\issue 1
\pages 283--296
\crossref{https://doi.org/10.1070/SM1995v083n01ABEH003590}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995TQ10000013}


Linking options:
  • http://mi.mathnet.ru/eng/msb935
  • http://mi.mathnet.ru/eng/msb/v185/i10/p145

    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

    This publication is cited in the following articles:
    1. V. Ya. Èiderman, “Estimates for potentials and $\delta$-subharmonic functions outside exceptional sets”, Izv. Math., 61:6 (1997), 1293–1329  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:231
    Full text:78
    References:33
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020