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pass92 December 19th, 2017 08:28 AM

Operator Fundamental solution
 
http://oi68.tinypic.com/317i4nt.jpg

Country Boy December 21st, 2017 05:56 AM

If $x> \xi$ then $|x- \xi|= x- \xi$ and $\frac{d^2|x-\xi|}{dx}= \frac{d^2(x- \xi)}{dx}= 0$. If $x< \xi$ then $|x- \xi|= -x+ \xi$ and $\frac{d^2|x-\xi|}{dx}= \frac{d^2(-x+\xi)}{dx}= 0$. The derivative, and so the second derivative, is not defined at $x= \xi$.

Now, what is the definition of "fundamental solution"?


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