The Proof of Theorem 10.2: The Smooth Case

  • Fritz Gesztesy
  • Marcus Waurick
Part of the Lecture Notes in Mathematics book series (LNM, volume 2157)


The principal aim of this chapter is to prove our most general version of the Callias index formula for L, stated in Theorem  10.2, in the special smooth case where \(\varPhi \in C_{b}^{\infty }(\mathbb{R}^{n}; \mathbb{C}^{d\times d})\) for some \(d \in \mathbb{N}\) (in addition to other conditions).


  1. 22.
    C. Callias, Axial anomalies and index theorems on open spaces. Commun. Math. Phys. 62, 213–234 (1978)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Fritz Gesztesy
    • 1
  • Marcus Waurick
    • 2
  1. 1.Dept of MathematicsUniversity of MissouriColumbiaUSA
  2. 2.Institut für AnalysisTU DresdenDresdenGermany

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