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Results tagged with fa.functional-analysis
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user 13093
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
3
votes
2
answers
1k
views
Sum of two closed operators closable
I found this question on another forum, and after processing it a bit, I didn't find a good answer. The question is:
Is the sum of two closed operators closable? If not, give an example of two clo …
- 2,222
2
votes
0
answers
175
views
A limit involving a regularizing kernel
I am studying the following article by Benoit Perthame: http://www.mendeley.com/research/uniqueness-error-estimates-first-order-quasilinear-conservation-laws-via-kinetic-entropy-defect-measure/#
Some …
- 2,222
1
vote
0
answers
134
views
Inequality involving BV norm and a regularizing kernel
In the same article by Benoit Perthame: http://www.mendeley.com/research/uniqueness-error-estimates-first-order-quasilinear-conservation-laws-via-kinetic-entropy-defect-measure/# (related to this ques …
- 2,222
1
vote
Are weak and strong convergence of sequences not equivalent?
A remark in H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Chapter 3:
In any infinite dimensional space the weak topology is strictly coarser than the strong t …
- 2,222
5
votes
1
answer
507
views
$C_0$-semigroups applications
My graduation thesis was about stability theorems for $C_0$-semigroups (see the Wikipedia article for the definitions: http://en.wikipedia.org/wiki/C0-semigroup). I would like to know if there is som …
- 2,222
7
votes
Accepted
How do people prove $\Gamma$-convergence in more complicated settings?
I am mostly familiar with the simpler definition ("Definition in first-countable spaces" from the Wikipedia link):
Given the functionals $F_\varepsilon, F: X \to \overline{\Bbb{R}}$
(indexed for $\va …
- 2,222
2
votes
Strange result about convexity
Here is a more problem solving approach, since this problem comes from AoPS. Instead of working with $f$, work with $g = f''$ which is a convex function.
Note that it is enough to assume $g(1)=0$. In …
- 2,222
9
votes
4
answers
2k
views
Books about capacity theory
While I was studying the book Variation et Optimisation de formes by Antoine Henrot and Michel Pierre, I encountered a section about the capacity associated to the $H^1$ norm, which is defined for eve …
- 2,222