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Heat kernel (PDE) asymptotic expansion

  1. Sep 7, 2009 #1
    let be the PDE eigenvalue problem [tex] \partial_{t} f =Hf [/tex]

    then if we define its Heat Kernel [tex] Z(u)= \sum_{n=0}^{\infty}e^{-uE_{n}} [/tex] valid only for positive 'u'

    then my question is how could get an asymptotic expansion of the Heat Kernel as u approaches to 0

    [tex] Z(u) \sim \sum_{n=0}^{\infty}a_{n} u^{n} [/tex] valid as u-->0+ (zero by the right)
  2. jcsd
  3. Sep 7, 2009 #2
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