- #1
zetafunction
- 391
- 0
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)
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)