Advertisement

Differential Equations

, Volume 48, Issue 12, pp 1577–1585 | Cite as

Elliptic translators on manifolds with point singularities

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

Abstract

We consider translators on manifolds with singularities of the type of a transversal intersection of smooth manifolds. We give the definition of ellipticity of translators, prove the finiteness (Fredholm property) theorem, and establish an index formula for the case of point singularities.

Keywords

Compact Operator Elliptic Operator Point Singularity Index Formula Fredholm Property 
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 and Parabolic Problems on Manifolds with Boundary Consisting of Components of Various Dimensions, Tr. Mosk. Mat. Obs., 1966, vol. 15, pp. 346–382.MathSciNetzbMATHGoogle Scholar
  2. 2.
    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
  3. 3.
    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
  4. 4.
    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
  5. 5.
    Savin, A.Yu. and Sternin, B.Yu., An Index Formula for Elliptic Translators, Dokl. Akad. Nauk, 2011, vol. 436, no. 4, pp. 443–447.Google Scholar
  6. 6.
    Sternin, B.Yu., Elliptic (Co)Boundary Morphisms, Dokl. Akad. Nauk SSSR, 1967, vol. 172, no. 1, pp. 44–47.Google Scholar
  7. 7.
    Novikov, S.P. and Sternin, B.Yu., Traces of Elliptic Operators on Submanifolds and K-Theory, Dokl. Akad. Nauk SSSR, 1966, vol. 170, no. 6, pp. 1265–1268.MathSciNetGoogle Scholar
  8. 8.
    Gokhberg, I.Ts. and Krein, M.G., Fundamental Aspects of Deficiency Numbers, Root Numbers, and Indexes of Linear Operators, Uspekhi Mat. Nauk, 1957, vol. 12, no. 2, pp. 43–118.zbMATHGoogle Scholar
  9. 9.
    Sternin, B.Yu., Kvaziellipticheskie operatory na beskonechnom tsilindre (Quasielliptic Operators on an Infinite Cylinder), Moscow, 1972.Google Scholar
  10. 10.
    Boo.-Bavnbek, B. and Wojciechowski, K., Elliptic Boundary Problems for Dirac Operators, Boston, 1993.Google Scholar
  11. 11.
    Plamenevskii, B.A., Algebry psevdodifferentsial’nykh operatorov (Algebras of Pseudodifferential Operators), Moscow: Nauka, 1986.Google Scholar
  12. 12.
    Nazaikinskii, V., Savin, A., Schulze, B.-W., and Sternin, B., Elliptic Theory on Singular Manifolds, Boca Raton, 2005.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

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

Personalised recommendations