RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Ufimsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






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


Ufimsk. Mat. Zh., 2012, Volume 4, Issue 1, Pages 122–135 (Mi ufa138)  

The angular distribution of zeros of random analytic functions

M. P. Maholaa, P. V. Filevychb

a Ya. S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NAS Ukraine, L'viv, Ukraine
b L'viv National University of Veterinary Medicine and Biotechnology, L'viv, Ukraine

Abstract: It is proved, that for the majority (in the sense of probability measure) of functions $f$, analytic in the unit disk with unbounded Nevanlinna characteristic $T_f(r)$, and for all $\alpha<\beta\le\alpha+2\pi$ the relation
$$ N_f(r,\alpha,\beta,0)\sim\frac{\beta-\alpha}{2\pi}T_f(r),\quad r\to1, $$
holds, where $N_f(r,\alpha,\beta,0)$ is the integrated counting functions of zeros of $f$ in the sector $ż\in\mathbb C\colon 0<|z|\le r, \alpha\le\arg_\alpha z<\beta\}$. The analogous proposition is obtained for entire functions under some conditions on their growth.

Keywords: analytic function, random analytic function, distribution of zeros, counting function, integrated counting function, Nevanlinna characteristic.

Full text: PDF file (467 kB)
References: PDF file   HTML file
UDC: 517.53
Received: 18.11.2011

Citation: M. P. Mahola, P. V. Filevych, “The angular distribution of zeros of random analytic functions”, Ufimsk. Mat. Zh., 4:1 (2012), 122–135

Citation in format AMSBIB
\Bibitem{MahFil12}
\by M.~P.~Mahola, P.~V.~Filevych
\paper The angular distribution of zeros of random analytic functions
\jour Ufimsk. Mat. Zh.
\yr 2012
\vol 4
\issue 1
\pages 122--135
\mathnet{http://mi.mathnet.ru/ufa138}


Linking options:
  • http://mi.mathnet.ru/eng/ufa138
  • http://mi.mathnet.ru/eng/ufa/v4/i1/p122

    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
  • Уфимский математический журнал
    Number of views:
    This page:211
    Full text:63
    References:15
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019