- #1
zetafunction
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let be the PDE eigenvalue problem \partial_{t} f =Hf
then if we define its Heat Kernel Z(u)= \sum_{n=0}^{\infty}e^{-uE_{n}} valid only for positive 'u'
then my question is how could get an asymptotic expansion of the Heat Kernel as u approaches to 0
Z(u) \sim \sum_{n=0}^{\infty}a_{n} u^{n} valid as u-->0+ (zero by the right)
then if we define its Heat Kernel Z(u)= \sum_{n=0}^{\infty}e^{-uE_{n}} valid only for positive 'u'
then my question is how could get an asymptotic expansion of the Heat Kernel as u approaches to 0
Z(u) \sim \sum_{n=0}^{\infty}a_{n} u^{n} valid as u-->0+ (zero by the right)