Advertisement

Differential Equations

, Volume 49, Issue 4, pp 494–509 | Cite as

Elliptic translators on manifolds with multidimensional singularities

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

Abstract

We consider translators on manifolds with many-dimensional singularities. We state the definition of ellipticity for translators, prove a finiteness (Fredholm property) theorem, and establish an index formula.

Keywords

Vector Bundle Boundary Operator Normal Bundle Fredholm Operator 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.
    Sternin, B.Yu., Elliptic Morphisms (Riggings of Elliptic Operators) for Submanifolds with Singularities, Dokl. Akad. Nauk SSSR, 1971, vol. 200, no. 1, pp. 45–48.MathSciNetGoogle Scholar
  2. 2.
    Sternin, B.Yu., Ellipticheskaya teoriya na kompaktnykh mnogoobraziyakh s osobennostyami (Elliptic Theory on Compact Manifolds with Singularities), Moscow: Moskov. Inst. Elektron. Mashinostroen., 1974.Google Scholar
  3. 3.
    Zelikin, M.I. and Sternin, B.Yu., A System of Integral Equations That Arises in the Problem of S. L. Sobolev, Sibirsk. Mat. Zh., 1977, vol. 18, no. 1, pp. 97–102.MathSciNetMATHGoogle Scholar
  4. 4.
    Savin, A.Yu. and Sternin, B.Yu., Elliptic Translators on Manifolds with Point Singularities, Differ. Uravn., 2012, vol. 48, no. 12, pp. 1612–1620.Google Scholar
  5. 5.
    Schulze, B.-W., Pseudodifferential Operators on Manifolds with Singularities, Amsterdam, 1991.Google Scholar
  6. 6.
    Luke, G., Pseudodifferential Operators on Hilbert Bundles, J. Differential Equations, 1972, vol. 12, pp. 566–589.MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Atiyah, M., Lektsii po K-teorii (Lectures on K-Theory), Moscow, 1967.Google Scholar
  8. 8.
    Nazaikinskii, V., Savin, A., Schulze, B.-W., and Sternin, B., Elliptic Theory on Singular Manifolds, Boca Raton, 2005.CrossRefGoogle Scholar
  9. 9.
    Gokhberg, I.Ts. and Krein, M.G., General Assertions on Deficiency Numbers and Indices of Linear Operators, Uspekhi Mat. Nauk, 1957, vol. 12, no. 2, pp. 43–118.MATHGoogle Scholar
  10. 10.
    Atiyah, M.F. and Bott, R., The Index Problem for Manifolds with Boundary, in Bombay Colloquium on Differential Analysis, Oxford, 1964, pp. 175–186.Google Scholar
  11. 11.
    Sternin, B.Yu., Kvaziellipticheskie operatory na beskonechnom tsilindre (Quasielliptic Operators on Infinite Cylinder), Moscow, 1972.Google Scholar
  12. 12.
    Erdélyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F.G., Higher Transcendental Functions (Bateman Manuscript Project), New York: McGraw-Hill, 1953. Translated under the title Vysshie transtsendentnye funktsii, Moscow, 1973, vol. 1.Google Scholar
  13. 13.
    Sternin, B.Yu., Quasielliptic Equations in an Infinite Cylinder, Dokl. Akad. Nauk SSSR, 1970, vol. 194, no. 5, pp. 1025–1028.MathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  • A. Yu. Savin
    • 1
    • 2
  • B. Yu. Sternin
    • 1
    • 2
  1. 1.Peoples’ Friendship University of RussiaMoscowRussia
  2. 2.Leibniz University of HannoverHannoverGermany

Personalised recommendations