Derivation of the Trace Formula: Diagonal Estimates

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• 刊名：Lecture Notes in Mathematics
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：2157
• 期：1
• 页码：77-99
• 全文大小：253 KB
• 参考文献：22.C. Callias, Axial anomalies and index theorems on open spaces. Commun. Math. Phys. 62, 213–234 (1978)MathSciNet CrossRef MATH
  35.J.B. Conway, Functions of One Complex Variable I, 2nd edn., 7th corr. printing (Springer, New York, 1995)
  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)MATH
  
• 作者单位：Fritz Gesztesy (14)
  Marcus Waurick (15)
  
  14. Dept of Mathematics, University of Missouri, Missouri, Columbia, USA
  15. Institut für Analysis, TU Dresden, Sachsen, Dresden, Germany
  
• 丛书名：The Callias Index Formula Revisited
• ISBN：978-3-319-29977-8
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Probability Theory and Stochastic Processes
  Dynamical Systems and Ergodic Theory
  Mathematical Biology
  Partial Differential Equations
  Functional Analysis
  Abstract Harmonic Analysis
  Group Theory and Generalizations
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1617-9692
• 卷排序：2157

文摘

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