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Annals of Global Analysis and Geometry

, Volume 16, Issue 2, pp 141–172 | Cite as

On the Index of Differential Operators on Manifolds with Conical Singularities

  • Bert-Wolfgang Schulze
  • Boris Sternin
  • Victor Shatalov
Article

Abstract

The paper contains the proof of the index formula for manifolds with conical points. For operators subject to an additional condition of spectral symmetry, the index is expressed as the sum of multiplicities of spectral points of the conormal symbol (indicial family) and the integral from the Atiyah–Singer form over the smooth part of the manifold. The obtained formula is illustrated by the example of the Euler operator on a two-dimensional manifold with conical singular point.

analytic index Atiyah–Singer theorem conical singularities ellipticity Eulercharacteristics Fredholm operators Mellintransform pseudodifferential operators regularizers trace class 

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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Bert-Wolfgang Schulze
    • 1
  • Boris Sternin
    • 2
  • Victor Shatalov
    • 2
  1. 1.MPAG "Analysis"Potsdam UniversityPotsdamGermany
  2. 2.Department of Computational Mathematics and CyberneticsMoscow State UniversityMoscowRussia

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