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Results tagged with fa.functional-analysis
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user 219013
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
3
votes
Accepted
Fundamental Theorem of Gamma-Convergence
Yes. Take any sequence $\{x_i\}$ for which $F(x_i)$ is bounded. For each $x_i$ consider the sequence satisfying (2), $\{x^\epsilon_i\}$ s.t. $x^\epsilon_i\to x_i$. Consider $x_i^{\epsilon_i}$ such tha …
- 231
1
vote
'Partial boundedness' of continuously parametrised power series
Take $D=[0,2]$, $a_i(x)=x^i$, then $f(x,1/3)$ converges for all $x\in D$, but $f(x,1)$ is unbounded as $x\to1$. So, unless I am misreading something in your question, the answer is negative.
EDIT: If …
- 231