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Results tagged with fa.functional-analysis
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user 124648
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
2
votes
1
answer
104
views
If $b\in C^1(E, \mathbb{R})$ and $b'$ is compact, then $b$ is weakly continuous — a referenc...
While reading the well known book Minimax Methods in Critical Point Theory with Applications to Differential Equations by Paul Rabinowitz, in the proof of a generalisation of the Mountain Pass Theorem …
2
votes
2
answers
411
views
The compact embedding of $H^{1/2}_{2\pi}$ in $L^s(0, 2\pi)$
Consider the fractional Sobolev space $H^{1/2}_{2\pi}$. This space consists of the functions $u$ in the space $L^2(0, 2\pi)$ whose coefficients of their Fourier expansion $$u(t)=a_0+\sum_{k=1}^{\infty …