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Results tagged with fa.functional-analysis
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user 119793
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
3
votes
1
answer
170
views
Infimum of an integral functional involving a symmetric matrix
I have a symmetric $d \times d$ matrix $A$ and I have the following functional:
$$
\mathcal J(h) := \int_{B_1(0)} \vert \langle Au,u \rangle\vert \frac{\vert h'(\vert u \vert)\vert}{\vert u \vert} du, …
- 391
6
votes
1
answer
212
views
A one-dimensional integral minimization problem
Let $\mathscr F$ be the collection of smooth functions $f \colon
\mathbb R \to \mathbb R$ such that
$f \in C^\infty_c(\mathbb R)$, with $\text{supp } f \subset [-1,1]$;
$\int_0^1 x f(x) …
- 391
4
votes
1
answer
178
views
Non-linear translation invariant functionals on $L^1$
I have recently come across a class of (possibly non-linear) operators $F$ defined on $L^1$ such that
$F \colon L^1(\mathbb R^d) \to \mathbb [0,+\infty]$;
$F(u(\cdot - z)) = F(u(\cdot))$ for every …
- 391