4
votes
0answers
114 views

About the convergence rate for an approximation to the heat kernel

Let $G(t,x)$ be the heat kernel $$ G(t,x)=\frac{1}{\sqrt{2\pi t}}e^{-\frac{x^2}{2t}}, \quad t>0, \:x\in\mathbb{R}. $$ Here is one approximation to $G(t,x)$: $$ G_\epsilon(t,x)=e^{-t/\epsilon} ...
3
votes
1answer
326 views

What do we know about the semigroup $e^{it\sqrt{-\Delta}}$

I'm very interested in the properties of the semigroup $e^{it\sqrt{-\Delta}}$, it may has some fundamental differences(such as the kernel) with the well-known schrodinger semigroup $e^{it\Delta}$. ...
4
votes
2answers
437 views

Reference on Semigroup Theory and Parabolics PDE'S

Recently started to study Semigroup Theory. My background is equivalent to the first three chapters of the Jack Hale's book, Asymptotic Behavior of Dissipative Systems. Looking for a reference to an ...