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Index of nonlocal problems associated with a bundle

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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.

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References

  1. Luke, G., Pseudodifferential Operators on Hilbert Bundles, J. Differential Equations, 1972, vol. 12, pp. 566–589.

    Article  MathSciNet  MATH  Google Scholar 

  2. Rozenblum, G., On Some Analytical Index Formulas Related to Operator-Valued Symbols, Electron. J. Differential Equations, 2002, vol. 17, pp. 1–31.

    MathSciNet  Google Scholar 

  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. Nazaikinskii, V., Savin, A., Schulze, B.-W., and Sternin, B., Elliptic Theory on Singular Manifolds, CRC, Boca Raton, 2005.

    Book  Google Scholar 

  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. 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.

    MathSciNet  MATH  Google Scholar 

  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.

    MathSciNet  Google Scholar 

  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. 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.

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to A. Yu. Savin.

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Original Russian Text © A.Yu. Savin, B.Yu. Sternin, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 8, pp. 1118–1127.

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Savin, A.Y., Sternin, B.Y. Index of nonlocal problems associated with a bundle. Diff Equat 50, 1112–1121 (2014). https://doi.org/10.1134/S0012266114080096

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  • DOI: https://doi.org/10.1134/S0012266114080096

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