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Results tagged with fa.functional-analysis
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user 125781
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
2
votes
0
answers
657
views
Intersection of Sobolev space with the space of continuous functions
While doing some problems, I came across the space $H=H^1(\Omega) \cap C(\Omega)$, where $\Omega$ is subset of $\mathbb{R^n}$. So far, by definition of these subspaces, We know that none of these are …
- 141
1
vote
0
answers
373
views
Fast growing unbounded functions in the Sobolev space $H^1(\Omega)$
I am looking for unbounded functions that grow rapidly fast near the origin, but are in the Sobolev space $H^1{(\Omega)}$, where $\Omega$ is a unit square centered at the origin.
I already know about …
- 141
1
vote
0
answers
52
views
Approximating norms using numerical integration? [closed]
I have a sequence of functions $u_m$ in $H^1(\Omega)$, where $\Omega$ is Lipschitz such that $u_m(x)=\int_{|y|\le \epsilon} \, f_m(x,y) \, dy$, but the integral cannot be expressed in terms of element …
- 141