Derivation of the Trace Formula: Diagonal Estimates

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


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


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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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