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Results tagged with fa.functional-analysis
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user 58975
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
3
votes
Gradient flows: convex potential vs. contractive flow?
It should be noticed that already on $R^d$ equipped with a non-Euclidean norm $\|.\|$ the answer to your question is no. Ohta-Sturm [1] proved the following: let $\lambda\in R$ and consider the classe …
- 660
7
votes
Accepted
About the metrizability of the space of Probability measures $\mathcal{P}(S)$
I'm not really sure what Villani wrote in his monograph, but it is true that one needs to prove that the weak topology is induced by a distance, as a priori it could be another topology with the same …
- 660
1
vote
Continuity and sequential continuity of a linear functional
Another way of seeing that the answer is affirmative is to realize that the topology on $E$ is the inductive limit of the topologies on $C(K,R^m)$ (see e.g. https://en.wikipedia.org/wiki/Final_topolog …
- 660
5
votes
1
answer
324
views
Convergence in energy of bounded (semi)subharmonic functions
Consider a sequence $(f_n)$ of functions in the flat torus $T^d$ converging Lebesgue-a.e. to a limit function $f$.
Assume that:
1) $|f_n|(x)\leq 1$ for every $n,x$
2) $\Delta f_n\geq -1$ in the sen …
- 660
3
votes
Convergence in energy of bounded (semi)subharmonic functions
I'm reporting an example, presented to me by Bozhidar Velichkov, showing that the answer to my question is no.
The example is based on a construction by Cioranescu-Murat given in their paper "Un ter …
- 660
5
votes
distributional Hessian for semiconvex functions on non-smooth manifolds
In $C^1$ manifolds I guess one could define measure-valued Hessian at least for $C^1$ functions by working in charts and throwing only one derivative on the $C^1$ test function.
In general $CD(K,N)$ …
- 660
8
votes
Accepted
Reference request: Wasserstein metric spaces for non linear weights/mobility?
Yes, this issue has been considered. You can start having a look at `A new class of transport distances between measures' by Dolbeault, Nazaret and Savaré (http://link.springer.com/article/10.1007%2F …
- 660