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Annals of Global Analysis and Geometry

, Volume 3, Issue 3, pp 337–383 | Cite as

Desuspension of splitting elliptic symbols I

  • Booss Bernhelm 
  • Wojciechowski Krzysztof 
Article

This paper provides an algorithm for the conversion of the index of an elliptic first-order differential operator A on the torus Y×S1 into the index of a canonically associated elliptic pseudo-differential operator Q and Y . It is supposed that Y is a closed smooth manifold and that A “splits” into ∂/∂t + Bt , where {Bt} is a family of self-adjoint elliptic operators on Y satisfying the periodicity condition B1 = g B0 g−1 for some unitary automorphism g . Then it will be shown that the operator Q ( the “desuspension” of A ) can be written down explicity in the form Q = P+ −gP where P+ are projections onto the space of Cauchy data. In the second part , applications are given for the calculation of the index of the general linear conjugation problem (“cutting and pasting” of elliptic operators) , and the intimate interrelations between the related procedures of algebraic topology, spectral theory and functional analysis are explained . Generalizations in various directions are indicated.

Keywords

Differential Operator Group Theory Periodicity Condition Spectral Theory Elliptic Operator 
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.

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Copyright information

© VEB Deutscher Verlag der Wissenschaften 1985

Authors and Affiliations

  • Booss Bernhelm 
    • 1
  • Wojciechowski Krzysztof 
    • 2
  1. 1.Institut for Studiet af Matematik og FysikRoskilde UniversitetscenterRoskilde
  2. 2.Instytut MatematycznyUniwersytet WarszawskiPKiN Warszawa

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