Timeline for Interpolation spaces

3 events

when toggle format	what		by	license	comment
Sep 7, 2017 at 14:41	comment	added	Mateusz Kwaśnicki		No, the condition $\sum \lambda_i^s \|a_i(f)\|^2 < \infty$ describes the domain of $(-\Delta)^{s/2}$. By the way, according to Encyclopedia of mathematics, the domain of $-\Delta$ is $H^2(\Omega) \cap H^1_0(\Omega)$ when $\Omega$ is a $C^2$ domain.
Sep 7, 2017 at 14:38	comment	added	Thomas		Thank you for your quick answer. If I understand correctly, in your argument $\sin x$ is not in $H_0^2(\Omega)$ since the derivative of this function is not zero on the boundary of the domain. In that case, if$\lambda_j$ are the eigenvalues of the Dirichlet laplacian, can we say $\left [ H_0^m(\Omega), L^2(\Omega)\right ]_\theta$ is the set of functions $f \in L^2(\Omega)$ such that $\sum_{i\geq 1} \lambda_i ^s a_i(f)^2<+\infty$, where $a_i(f)=\langle f, \phi_i \rangle$ and $\phi_i$ is the associated eigenfunction.
Sep 7, 2017 at 14:16	history	answered	Mateusz Kwaśnicki	CC BY-SA 3.0