Mathematics of the USSR-Izvestiya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Mathematics of the USSR-Izvestiya, 1977, Volume 11, Issue 6, Pages 1285–1322
DOI: https://doi.org/10.1070/IM1977v011n06ABEH001769
(Mi im2073)
 

This article is cited in 6 scientific papers (total in 6 papers)

On the Dirichlet problem for a pseudodifferential equation encountered in the theory of random processes

B. V. Pal'tsev
References:
Abstract: The problem is considered of finding a function $u(t)$ satisfying the equation
\begin{equation} \mathscr F^{-1}[\tilde k(x)\tilde u(x)](t)=f(t)\quad\text{for}\quad t\in\Omega,\qquad\tilde u(x)=\mathscr F[u(t)](x), \end{equation}
and the conditions
\begin{equation} u(t)\equiv0\quad\text{for}\quad t\notin\Omega,\qquad\int_{-\infty}^{+\infty}\tilde k(x)|\tilde u(x)|^2\,dx<\infty, \end{equation}
where $\tilde k(x)$ is a nonnegative measurable function and $\mathscr F$ is the Fourier operator. An existence and uniqueness theorem is proved under quite general assumptions concerning the spectral densities $\tilde k(x)$. Explicit formulas for the solution of problem (1), (2) are obtained in the case when $\Omega$ is an interval $(-T,T)$ and $\tilde k(x)=|x|^\alpha$, $\alpha>0$.
Bibliography: 17 titles.
Received: 23.09.1976
Bibliographic databases:
UDC: 517.9
MSC: Primary 35S15; Secondary 60G25, 62M20
Language: English
Original paper language: Russian
Citation: B. V. Pal'tsev, “On the Dirichlet problem for a pseudodifferential equation encountered in the theory of random processes”, Math. USSR-Izv., 11:6 (1977), 1285–1322
Citation in format AMSBIB
\Bibitem{Pal77}
\by B.~V.~Pal'tsev
\paper On the Dirichlet problem for a~pseudodifferential equation encountered in the theory of random processes
\jour Math. USSR-Izv.
\yr 1977
\vol 11
\issue 6
\pages 1285--1322
\mathnet{http://mi.mathnet.ru//eng/im2073}
\crossref{https://doi.org/10.1070/IM1977v011n06ABEH001769}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=499862}
\zmath{https://zbmath.org/?q=an:0372.35074|0396.35089}
Linking options:
  • https://www.mathnet.ru/eng/im2073
  • https://doi.org/10.1070/IM1977v011n06ABEH001769
  • https://www.mathnet.ru/eng/im/v41/i6/p1348
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024