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Algebras of Singular Integral Operators with Shift

  • Israel Gohberg
  • Nahum Krupnik
Part of the Operator Theory: Advances and Applications book series (OT, volume 206)

Abstract

In this note the results of [1] are generalized to the case of an arbitrary simple closed Lyapunov contour and an arbitrary Carleman shift changing the orientation of the contour.

Keywords

Banach Space Unit Circle Operator Theory English Translation Singular Integral Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    I.C. Gohberg and N.Ya. Krupnik, One-dimensional singular integral operators with shift. Izv. Akad. Nauk Arm. SSR, Ser. Matem. 8 (1973), no. 1, 3–12 (in Russian). English translation: this volume. MR0333840 (48 #12162), Zbl 0255.47058.MathSciNetGoogle Scholar
  2. [2]
    I.C. Gohberg and N.Ya. Krupnik, Introduction to the Theory of One-Dimensional Singular Integral Operators. Shtiinca, Kishinev, 1973 (in Russian). MR0405177 (53 #8971), Zbl 0271.47017. German translation: Einführung in die Theorie der Eindimensionalen Singulären Integraloperatoren. Birkhäuser Verlag, Basel, Boston, 1979. MR0545507 (81d:45010), Zbl 0413.47040. English translation (from the German edition of 1979) was revised and separated into two volumes: One-Dimensional Linear Singular Integral Equations. I. Introduction. Operator Theory: Advances and Applications, 53. Birkhäuser Verlag, Basel, 1992. MR1138208 (93c:47061), Zbl 0743.45004. One-Dimensional Linear Singular Integral Equations. II. General Theory and Applications. Operator Theory: Advances and Applications, 54. Birkhäuser Verlag, Basel, 1992. MR1182987 (93k:47059), Zbl 0781.47038.Google Scholar
  3. [3]
    I.C. Gohberg and N.Ya. Krupnik, Singular integral operators with piecewise continuous coefficients and their symbols. Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 940–964 (in Russian). English translation: Math. USSR Izvestiya 5 (1971), no. 4, 955–979. MR0291893 (45 #981), Zbl 0235.47025.MathSciNetGoogle Scholar
  4. [4]
    I.C. Gohberg and N.Ya. Krupnik, Banach algebras generated by singular integral operators. In: “Hilbert Space Operators Operator Algebras (Proc. Internat. Conf., Tihany, 1970).” Colloquia Math. Soc. Janos Bolyai 5 (1972), 239–264. MR0380519 (52 #1419), Zbl 0354.45008.MathSciNetGoogle Scholar

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • Israel Gohberg
  • Nahum Krupnik

There are no affiliations available

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