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Results tagged with fa.functional-analysis
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user 25266
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
4
votes
1
answer
2k
views
Composition of $C^{k, \alpha}$ function with $C^\infty$ function on a compact domain
(I asked this question on MSE but I did not receive an answer so I hope I can post here.)
Let $S$ be a compact set in $\mathbb{R}^2$ and let $C^{k, \alpha}(S)$ denote the usual Holder space with $k$ …
- 67
1
vote
1
answer
2k
views
Basic questions about parabolic Holder space
Hi, I am interested in learning a bit more about this space. I have exhausted all the books available at my disposal, and none of them explain much of the basics for me. Here's a definition of this sp …
- 67
1
vote
1
answer
3k
views
How to show this Holder bound?
Define the seminorm on the space $S=[0,1]\times[0,T]$
$$\mid u\mid_{\alpha} = \sup\frac{|u(x, t) - u(y,s)|}{(|x-y|^2 + |t-s|)^{\frac{\alpha}{2}}}.$$
Define the norms on the same space
$$\lVert u \rVer …
- 67