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Izv. Akad. Nauk SSSR Ser. Mat., 1980, Volume 44, Issue 2, Pages 322–394 (Mi izv1669)  

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

Convolution equations on a finite interval for a class of symbols having powerlike asymptotics at infinity

B. V. Pal'tsev


Abstract: A class of convolution equations is introduced on a finite interval, which is a generalization of a series of examples encountered in mathematical physics and other fields and for which a certain analogue of the Wiener–Hopf method is developed. As a corollary the Fredholm property is established for general convolution operators on a finite interval with symbols having polynomial growth at infinity in Sobolev spaces of generalized functions.
Bibliography: 31 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1981, 16:2, 291–356

Bibliographic databases:

UDC: 517.968.72 + 53
MSC: Primary 45E10; Secondary 47A53
Received: 10.10.1979

Citation: B. V. Pal'tsev, “Convolution equations on a finite interval for a class of symbols having powerlike asymptotics at infinity”, Izv. Akad. Nauk SSSR Ser. Mat., 44:2 (1980), 322–394; Math. USSR-Izv., 16:2 (1981), 291–356

Citation in format AMSBIB
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\by B.~V.~Pal'tsev
\paper Convolution equations on a finite interval for a class of symbols
having powerlike asymptotics at infinity
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1980
\vol 44
\issue 2
\pages 322--394
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=571101}
\zmath{https://zbmath.org/?q=an:0458.45003|0431.45007}
\transl
\jour Math. USSR-Izv.
\yr 1981
\vol 16
\issue 2
\pages 291--356
\crossref{https://doi.org/10.1070/IM1981v016n02ABEH001309}
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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  mathnet  crossref  mathscinet  zmath
    2. 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  mathnet  crossref  mathscinet  zmath
    3. 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  mathnet  crossref  mathscinet  zmath
    4. V. M. Kaplitskii, “An integral equation with matrix difference kernel on an interval”, Sb. Math., 189:8 (1998), 1171–1177  mathnet  crossref  crossref  mathscinet  zmath  isi
    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  mathnet  crossref  crossref  mathscinet  zmath  isi
    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  mathnet  crossref  mathscinet  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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