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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.
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
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