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Results tagged with banach-spaces
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user 61771
A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.
2
votes
Accepted
Banach space-valued test functions in the definition of a weak solution of a PDE problem
Writing your equation (3) as $a(u,\psi)=0$, it is indeed common to call $u\in L^1_\mathrm{loc}$ a `weak solution' to your problem if and only it satisfies
$$
a(u,\psi) = 0 \mbox{ for all } \psi \in …
- 778
1
vote
Spectra on different spaces
I know it's a while since this question was asked, but I think the book "Linear Operators and their Spectra" by E. Brian Davies might contain some information about what's being asked here. In particu …
- 778