Abstract
The small time asymptotics of the kernel ofe −tH is defined and derived for\(H = \frac{{d^2 }}{{dx^2 }} + \frac{\kappa }{{x^2 }}\) on ℝ1. Lemmas on singular asymptotics in the sense of distributions are formulated and used. The results are applied to derive an index formula on ℝ1.
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My ideas about the interpretation of the trace formulas grew out of conversations with S. Trahanas
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Communicated by A. Jaffe
Work partly supported by the National Science Foundation Grant No. 80-08894 MCS
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Callias, C.J. The heat equation with singular coefficients. Commun.Math. Phys. 88, 357–385 (1983). https://doi.org/10.1007/BF01213214
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DOI: https://doi.org/10.1007/BF01213214