Advertisement

Differential Equations

, Volume 50, Issue 8, pp 1112–1121 | Cite as

Index of nonlocal problems associated with a bundle

  • A. Yu. Savin
  • B. Yu. Sternin
Partial Differential Equations
  • 30 Downloads

Abstract

We study operators associated with a bundle with compact base and fiber. We construct an algebra of such operators. For elliptic elements of the algebra, we prove the finiteness theorem and derive an index formula.

Keywords

Boundary Operator Total Space Fredholm Operator Nonlocal Problem Index Formula 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Luke, G., Pseudodifferential Operators on Hilbert Bundles, J. Differential Equations, 1972, vol. 12, pp. 566–589.MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Rozenblum, G., On Some Analytical Index Formulas Related to Operator-Valued Symbols, Electron. J. Differential Equations, 2002, vol. 17, pp. 1–31.MathSciNetGoogle Scholar
  3. 3.
    Rozenblum, G., Regularization of Secondary Characteristic Classes and Unusual Index Formulas for Operator-Valued Symbols, in Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations, vol. 145 of Oper. Theory Adv. Appl. Basel, 2003, pp. 419–437.Google Scholar
  4. 4.
    Nazaikinskii, V., Savin, A., Schulze, B.-W., and Sternin, B., Elliptic Theory on Singular Manifolds, CRC, Boca Raton, 2005.CrossRefGoogle Scholar
  5. 5.
    Sternin, B.Yu. and Shatalov, V.E., Extension of the Algebra of Pseudodifferential Operators, and Some Nonlocal Elliptic Problems, Mat. Sb., 1994, vol. 185, no. 3, pp. 117–159.Google Scholar
  6. 6.
    Sternin, B.Yu., Elliptic and Parabolic Problems on Manifolds with a Boundary Consisting of Components of Different Dimension, Tr. Mosk. Mat. Obs., 1966, vol. 15, pp. 346–382.MathSciNetMATHGoogle Scholar
  7. 7.
    Sternin, B.Yu., Relative Elliptic Theory, and S. L. Sobolev’s Problem, Dokl. Akad. Nauk SSSR, 1976, vol. 230, no. 2, pp. 287–290.MathSciNetGoogle Scholar
  8. 8.
    Savin, A.Yu. and Sternin, B.Yu., Nonlocal Elliptic Operators for Compact Lie Groups, Dokl. Akad. Nauk, 2010, vol. 431, no. 4, pp. 457–460.Google Scholar
  9. 9.
    Sternin, B.Yu., On a Class of Nonlocal Elliptic Operators for Compact Lie Groups. Uniformization and Finiteness Theorem, Cent. Eur. J. Math., 2011, vol. 9, no. 4, pp. 814–832.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Peoples’ Friendship University of RussiaMoscowRussia
  2. 2.Leibniz Universität HannoverHannoverGermany

Personalised recommendations