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On applicability of the projection method to two-dimensional Toeplitz operators with measurable symbol

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Abstract

For some class of two-dimensional Toeplitz operators with locally sectorial symbol, we establish a criterion for the projection method to possess the Fredholm property.

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References

  1. Simonenko I. B., “A new general method for studying linear operator equations analogous to singular integral equations. I,” Izv. Akad. Nauk SSSR Ser. Mat., 29, No. 3, 567–586 (1965).

    MATH  MathSciNet  Google Scholar 

  2. Böttcher A. and Silbermann B., Analysis of Toeplitz Operators, Akad.-Verl., Berlin (1989).

    Google Scholar 

  3. Gokhberg I. Ts. and Krupnik N. Ya., An Introduction to the Theory of One-Dimensional Singular Integral Operators [in Russian], Shtiintsa, Kishinëv (1973).

    Google Scholar 

  4. Pilidi V. S., “On many-dimensional singular operators,” Dokl. Akad. Nauk SSSR, 201, No. 4, 1723–1726 (1971).

    MATH  MathSciNet  Google Scholar 

  5. Kozak A. V., “The local principle in the theory of projection methods,” Dokl. Akad. Nauk SSSR, 212, No. 6, 1287–1289 (1973).

    MATH  MathSciNet  Google Scholar 

  6. Sazonov L. I., “Bisingular characteristic operators with discontinuous coefficients in the space L 2(R 2),” Funktsional. Anal. Prilozhen., 19, No. 2, 90–91 (1985).

    MATH  MathSciNet  Google Scholar 

  7. Sazonov L. I., “On bisingular operators with measurable coefficients,” Siberian Math. J., 37, No. 2, 335–344 (1996).

    Article  MATH  MathSciNet  Google Scholar 

  8. Gokhberg I. Ts. and Fel’dman I. A., Equations in Convolutions and Projection Methods of Their Solution [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  9. Dixmier J., C*-Algebras and Their Representations [Russian translation], Nauka, Moscow (1974).

    Google Scholar 

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Authors and Affiliations

  1. Rostov State University, Rostov-on-Don, Russia

    L. I. Sazonov

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  1. L. I. Sazonov
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Original Russian Text Copyright © 2006 Sazonov L. I.

The author was supported by the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-1768.2003.1).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 47, No. 3, pp. 636–648, May–June, 2006.

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Sazonov, L.I. On applicability of the projection method to two-dimensional Toeplitz operators with measurable symbol. Sib Math J 47, 526–536 (2006). https://doi.org/10.1007/s11202-006-0064-z

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  • DOI: https://doi.org/10.1007/s11202-006-0064-z

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