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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

1 vote
0 answers
158 views

Interpolation of Sobolev spaces with constraints

Let us consider a real interval $[0, L]$, with $a\in (0, L)$, and let $I_1=(0, a)$ and $I_2=(a, L)$. We denote by $H^k(I_1)$ and $H^k(I_2)$ the usual Sobolev spaces, defined for $k\in \mathbb{N}$. Now …
rebo79's user avatar
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2 votes
0 answers
211 views

Interpolation of embedded Hilbert spaces and intersection

I'm wondering under what hypothesis it is true a property like $$[\mathcal{H}_1\cap X, \mathcal{H}_2\cap X]_{\theta}=\mathcal{H}_1\cap X\cap [\mathcal{H}_1, \mathcal{H_2}]_{\theta}$$ where $\mathcal{H …
rebo79's user avatar
  • 81