mhill
Aug16-08, 06:18 PM
let be the identity
(2 \pi ) i^{m-1}D^{m} \delta (u) = \int_{-\infty}^{\infty} dx e^{iux}x^{m-1} `
then making the replacement u=e^D D derivative with respect to 'x' then
(2 \pi ) i^{m-1}D^{m} \delta (e^{D})f(0) = \int_{-\infty}^{\infty} dx e^{ixe^{D}}x^{m-1}f(0)=\int_{-\infty}^{\infty} dx x^{m-1}\sum_{k=0}^{\infty}\frac{i^{k}f(n)}{n!}
the problem is that i do not know how to define D^{m} \delta (e^{D})
(2 \pi ) i^{m-1}D^{m} \delta (u) = \int_{-\infty}^{\infty} dx e^{iux}x^{m-1} `
then making the replacement u=e^D D derivative with respect to 'x' then
(2 \pi ) i^{m-1}D^{m} \delta (e^{D})f(0) = \int_{-\infty}^{\infty} dx e^{ixe^{D}}x^{m-1}f(0)=\int_{-\infty}^{\infty} dx x^{m-1}\sum_{k=0}^{\infty}\frac{i^{k}f(n)}{n!}
the problem is that i do not know how to define D^{m} \delta (e^{D})