Communications in Mathematical Physics

, Volume 88, Issue 3, pp 357–385 | Cite as

The heat equation with singular coefficients

I. Operators of the form\( - \frac{{d^2 }}{{dx^2 }} + \frac{\kappa }{{x^2 }}\) in dimension 1
  • Constantine J. Callias


The small time asymptotics of the kernel ofetH 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.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Heat Equation 
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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Constantine J. Callias
    • 1
  1. 1.Department of MathematicsColumbia UniversityNew YorkUSA

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