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Results tagged with fa.functional-analysis
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user 8353
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
14
votes
The role of completeness in Hilbert Spaces
It's interesting the way that you phrase the question. I always thought of Hilbert spaces as Banach spaces with extra structure and just took for granted that completeness is always desirable. (Banach …
- 343
1
vote
1
answer
304
views
variational formulation: boundedness of the bilinear form
The simplest case of the problem I'm thinking about involves an elliptic differential operator, $Lu = -u'' + qu$, on the interval $(0,1)$, with homogeneous Dirichlet boundary conditions. I want to sho …
- 343
2
votes
When is a finite matrix a "good" approximate representation of an operator?
The answer to your question, "are there conditions on the discrete representation ... to detect whether or not a given claimed representation $J$ is 'good'...", is yes. One usually measures "good" in …
- 343