Tagged Questions
3
votes
1answer
81 views
What is the use of $H_s$ for non-integer $s$?
So we have the whole set of theory for Sobolev spaces \begin{equation}
H_s(\mathbb{R}^d)=\{u\in D'(\mathbb{R}^d):(1+|y|^2)^{s/2}\hat{u}\in\mathcal{L}^2(\mathbb{R}^d)\},
\end{equation} and we know that ...
2
votes
1answer
44 views
So $k^2-\Delta: H_{s+2}\to H_{s}$ is a homeomorphism, but what does that tell us?
For each $t\in\mathbb{R}$, we define the Sobolev space \begin{equation}
H_t=\{u\in\mathcal{S}':\int(1+|y|^2)^t|\hat{u}(y)|^2dy<+\infty\},
\end{equation} where $\mathcal{S}'$ is the space of ...
0
votes
1answer
73 views
How does a myopic interpret Wiener's Tauberian?
I just read about this post on the intuition behind convolution. In Terence Tao's answer convolution is interpreted as the blur of image in near-sighted eyes. In Harald Hanche-Olsen's it is made ...
