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Pseudodifferential Subspaces and Their Applications in Elliptic Theory

  • Anton Savin
  • Boris Sternin
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Part of the Trends in Mathematics book series (TM)

Abstract

The aim of this paper is to explain the notion of subspace defined by means of pseudodifferential projection and give its applications in elliptic theory. Such subspaces are indispensable in the theory of well-posed boundary value problems for an arbitrary elliptic operator, including the Dirac operator, which has no classical boundary value problems. Pseudodifferential subspaces can be used to compute the fractional part of the spectral Atiyah73-Patodi— Singer eta invariant, when it defines a homotopy invariant (Gilkey’s problem). Finally, we explain how pseudodifferential subspaces can be used to give an analytic realization of the topological K-group with finite coefficients in terms of elliptic operators. It turns out that all three applications are based on a theory of elliptic operators on closed manifolds acting in subspaces.

Keywords

elliptic operator boundary value problem pseudodifferential subspace dimension functional η-invariant index modn-index parity condition 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • Anton Savin
    • 1
  • Boris Sternin
    • 1
  1. 1.Independent University of MoscowMoscowRussia

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