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Derivation of the Trace Formula: Diagonal Estimates

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

Abstract

This chapter is a direct continuation of the preceding one and computes the actual trace of the operator \(\chi _{\varLambda }B_{L}(z) = z\chi _{\varLambda }\mathop{\mathrm{tr}}\nolimits _{N}\big(\left (L^{{\ast}}L + z\right )^{-1} -\left (LL^{{\ast}} + z\right )^{-1}\big)\) for odd space dimensions n. An application of Montel’s theorem plays a decisive role in this trace computation, in addition it should be noted that the case n = 3 is more subtle than \(n\geqslant 5\) and requires special attention to follow in Chap.  9

References

  1. 22.
    C. Callias, Axial anomalies and index theorems on open spaces. Commun. Math. Phys. 62, 213–234 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 35.
    J.B. Conway, Functions of One Complex Variable I, 2nd edn., 7th corr. printing (Springer, New York, 1995)Google Scholar
  3. 57.
    I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products, corrected and enlarged edition, prepared by A. Jeffrey (Academic Press, San Diego, 1980)zbMATHGoogle 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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