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 Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 6, Pages 1348–1387 (Mi izv2073)

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

B. V. Pal'tsev

Abstract: The problem is considered of finding a function $u(t)$ satisfying the equation
and the conditions
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.

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English version:
Mathematics of the USSR-Izvestiya, 1977, 11:6, 1285–1322

Bibliographic databases:

UDC: 517.9
MSC: Primary 35S15; Secondary 60G25, 62M20

Citation: B. V. Pal'tsev, “On the Dirichlet problem for a pseudodifferential equation encountered in the theory of random processes”, Izv. Akad. Nauk SSSR Ser. Mat., 41:6 (1977), 1348–1387; 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 Izv. Akad. Nauk SSSR Ser. Mat. \yr 1977 \vol 41 \issue 6 \pages 1348--1387 \mathnet{http://mi.mathnet.ru/izv2073} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=499862} \zmath{https://zbmath.org/?q=an:0372.35074|0396.35089} \transl \jour Math. USSR-Izv. \yr 1977 \vol 11 \issue 6 \pages 1285--1322 \crossref{https://doi.org/10.1070/IM1977v011n06ABEH001769} 

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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. B. V. Pal'tsev, “A generalization of the Wiener–Hopf method for convolution equations on a finite interval with symbols having power-like asymptotics at infinity”, Math. USSR-Sb., 41:3 (1982), 289–328
2. B. V. Pal'tsev, “Convolution equations on a finite interval for a class of symbols having powerlike asymptotics at infinity”, Math. USSR-Izv., 16:2 (1981), 291–356
3. B. V. Pal'tsev, “A method for constructing a canonical matrix of solutions of a Hilbert problem arising in the solution of convolution equations on a finite interval”, Math. USSR-Izv., 19:3 (1982), 559–610
4. Yu. I. Karlovich, I. M. Spitkovsky, “Factorization of almost periodic matrix-valued functions and the Noether theory for certain classes of equations of convolution type”, Math. USSR-Izv., 34:2 (1990), 281–316
5. B. V. Pal'tsev, “Asymptotic behaviour of the spectra of integral convolution operators on a finite interval with homogeneous polar kernels”, Izv. Math., 67:4 (2003), 695–779
6. M. K. Kerimov, “Boris Vasil'evich Pal'tsev (on the occasion of his seventieth birthday)”, Comput. Math. Math. Phys., 50:7 (2010), 1113–1119
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