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Izv. Akad. Nauk SSSR Ser. Mat., 1983, Volume 47, Issue 5, Pages 1030–1077 (Mi izv1435)  

This article is cited in 11 scientific papers (total in 11 papers)

An algebra of singular integral operators with piecewise-continuous coefficients and a piecewise-smooth shift on a composite contour

Yu. I. Karlovich, V. G. Kravchenko


Abstract: A method is developed for investigating the Noetherian property of operators of a particular kind, prototypes of which are singular integral operators with a shift (SIOS). The algebra of symbols of SIOS is constructed. Questions of invertibility of the symbols are considered. Algorithms are obtained for verifying conditions for the Noetherian property and for computing the index of SIOS.
Bibliography: 31 titles.

Full text: PDF file (5014 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1984, 23:2, 307–352

Bibliographic databases:

UDC: 517.948.32
MSC: Primary 45P05, 47G05, 47A53; Secondary 45E99
Received: 30.09.1981

Citation: Yu. I. Karlovich, V. G. Kravchenko, “An algebra of singular integral operators with piecewise-continuous coefficients and a piecewise-smooth shift on a composite contour”, Izv. Akad. Nauk SSSR Ser. Mat., 47:5 (1983), 1030–1077; Math. USSR-Izv., 23:2 (1984), 307–352

Citation in format AMSBIB
\Bibitem{KarKra83}
\by Yu.~I.~Karlovich, V.~G.~Kravchenko
\paper An algebra of singular integral operators with piecewise-continuous coefficients and a~piecewise-smooth shift on a~composite contour
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1983
\vol 47
\issue 5
\pages 1030--1077
\mathnet{http://mi.mathnet.ru/izv1435}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=718415}
\zmath{https://zbmath.org/?q=an:0565.47009}
\transl
\jour Math. USSR-Izv.
\yr 1984
\vol 23
\issue 2
\pages 307--352
\crossref{https://doi.org/10.1070/IM1984v023n02ABEH001773}


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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. 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
    2. Karlovich I., “On Algebras of Singular Integral-Operators with Discrete-Groups of Shifts in Lp Spaces”, 304, no. 2, 1989, 274–280  zmath  isi
    3. A. Of Böttcher Chemnitz, Yu. I. Karlovich, B. Silbermann, “Singular Integral Equations with PQC Coefficients and Freely Transformed Argument”, Math Nachr, 166:1 (1994), 113  crossref  mathscinet  isi
    4. Karlovich Y.I., de A.rellano E.R., “Singular integral operators with fixed singularities on weighted Lebesgue spaces”, Integral Equations and Operator Theory, 48:3 (2004), 331–363  crossref  isi  elib
    5. M.A. Bastos, C.A. Fernandes, Y.I. Karlovich, “Spectral measures in -algebras of singular integral operators with shifts”, Journal of Functional Analysis, 242:1 (2007), 86  crossref
    6. Karlovich Yu.I., “Nonlocal singular integral operators with slowly oscillating data”, Operator Algebras, Operator Theory and Applications, Operator Theory : Advances and Applications, 181, 2008, 229–261  isi
    7. B. T. Bilalov, “A system of exponential functions with shift and the Kostyuchenko problem”, Siberian Math. J., 50:2 (2009), 223–230  mathnet  crossref  mathscinet  isi  elib
    8. M. A. Bastos, C. A. Fernandes, Yu. I. Karlovich, “A Nonlocal C*-Algebra of Singular Integral Operators with Shifts Having Periodic Points”, Integr. Equ. Oper. Theory, 2011  crossref
    9. B. T. Bilalov, “On solution of the Kostyuchenko problem”, Siberian Math. J., 53:3 (2012), 404–418  mathnet  crossref  mathscinet  isi
    10. M.A. Bastos, C.A. Fernandes, Yu.I. Karlovich, “A -algebra of singular integral operators with shifts admitting distinct fixed points”, Journal of Mathematical Analysis and Applications, 2013  crossref
    11. Karlovich Yu.I., “The Haseman Boundary Value Problem With Slowly Oscillating Coefficients and Shifts”, Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics: the Albrecht Bottcher Anniversary Volume, Operator Theory Advances and Applications, 259, eds. Bini D., Ehrhardt T., Karlovich A., Spitkovsky I., Springer International Publishing Ag, 2017, 463–500  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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