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Results tagged with fa.functional-analysis
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user 13904
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
1
vote
1
answer
2k
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Lipschitz functions and $W^{1,\infty}$
I am not sure my question is research type, but I am sure I can find here an answer.
So we have the following theorem in the book of Lawrence Evans in PDE, 2nd edition pages 294-295:
Theorem 4 (C …
- 1,594
-1
votes
1
answer
128
views
Proving convergence of an integral-differential equation [closed]
I have a second order nonlinear ordinary differential equation which I transformed into an integral-differential equation by multiplying the ODE by $y'$ and integrating.
My question is where can I fi …
- 1,594
5
votes
0
answers
236
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Is Akcoglu's theorem for power bounded positive operators still an open problem?
I am reading Ulrich Krengel's book, Ergodic Theorems; the theorem of Akcoglu's he mentions of is on page 189, theorem 2.5.
" If $T$ is a positive contraction in a space $L_p$ with $1<p<\infty$, then: …
- 1,594
0
votes
1
answer
260
views
Banach space dual to $L^\infty(I,H^1(M))$
What is the dual to $L^\infty (I,H^1(M))$?, where $I$ is an interval in the real line; $H^1(M)$ is Sobolev space of degree 1, and $M$ is a compact manifold like the torus.
Any references that show th …
- 1,594
1
vote
0
answers
80
views
boundedness of a sequence $ \in L^{\infty}(I,H^1(M))\cap Lip(I,L^2(M))$ implies that its tem... [closed]
Hi I have the next claim which I would like to find a proof of it.
I have a sequence of functions $u_\epsilon(t,x) \in H^1(M)$ where $M$ is a compact manifold, and $u_\epsilon \in L^\infty(I,H^1(M))\ …
- 1,594