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Multidimensional integral operators with bihomogeneous kernels: A projection method and pseudospectra

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Abstract

We consider multidimensional integral operators with bihomogeneous and rotation invariant kernels. For such operators we obtain a criterion for applicability of a projection method in the scalar and matrix cases and describe the limit behavior of the ε-pseudospectra of the truncated operators \(A_{\tau _1 , \tau _2 } \) as τ 1 → 0 and τ 2 → 0.

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References

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

    Google Scholar 

  2. Böttcher A. and Silbermann B., Analysis of Toeplitz Operators, Springer-Verlag, Berlin; Heidelberg; New York (1990).

    Google Scholar 

  3. Hagen R., Roch S., and Silbermann B., Spectral Theory of Approximation Methods for Convolution Equations, Birkhäuser, Basel; Boston; Berlin (1995).

    Google Scholar 

  4. Böttcher A., “Pseudospectra and singular values of large convolution operators,” J. Integral Equations Appl., 6, 267–301 (1994).

    MATH  MathSciNet  Google Scholar 

  5. Avsyankin O. G. and Karapetyants N. K., “A projection method in the theory of integral operators with homogeneous kernels,” Mat. Zametki, 75, No. 2, 163–172 (2004).

    MathSciNet  Google Scholar 

  6. Avsyankin O. G., “Applicability of the projection method to pair integral operators with homogeneous kernels,” Russian Math., 46, No. 8, 1–5 (2002).

    MATH  MathSciNet  Google Scholar 

  7. Avsyankin O. G. and Karapetyants N. K., “On the pseudospectra of multidimensional integral operators with homogeneous kernels of degree-n,” Siberian Math. J., 44, No. 6, 935–950 (2003).

    Article  MathSciNet  Google Scholar 

  8. Avsyankin O. G. and Deundyak V. M., “On calculation of the index of multidimensional integral operators with bihomogeneous kernels,” Dokl. Ross. Akad. Nauk, 391, No. 1, 7–9 (2003).

    MathSciNet  Google Scholar 

  9. Karapetiants N. and Samko S., Equations with Involutive Operators, Birkhäuser, Boston; Basel; Berlin (2001).

    Google Scholar 

  10. Murphy G., C*-Algebras and Operator Theory [Russian transaltion], Faktorial, Moscow (1997).

    Google Scholar 

  11. Böttcher A. and Grudsky S. M., Toeplitz Matrices, Asymptotic Linear Algebra and Functional Analysis, Birkhäuser, Boston; Basel; Berlin (2000).

    Google Scholar 

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Authors and Affiliations

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

    O. G. Avsyankin

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  1. O. G. Avsyankin
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Original Russian Text Copyright © 2006 Avsyankin O. G.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 47, No. 3, pp. 501–513, May–June, 2006.

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Avsyankin, O.G. Multidimensional integral operators with bihomogeneous kernels: A projection method and pseudospectra. Sib Math J 47, 410–421 (2006). https://doi.org/10.1007/s11202-006-0053-2

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  • DOI: https://doi.org/10.1007/s11202-006-0053-2

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