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Results tagged with fa.functional-analysis
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user 51335
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
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Ball in separable Banach space has positive Gaussian measure
I have (presumably non-degenerate) Gaussian $\mu$ over separable Banach space $X$. I would like to prove that for any ball of radius $r$ centered at $x$, $\mu(B_r(x))$. I know how to prove this in th …
- 128k
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Conditional Gaussians in infinite dimensions
I asked this over on cross validated, but thought it might also get an answer here:
The law of the conditional Gaussian distribution (the mean and covariance) are frequently mentioned to extend to the …
- 128k
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Hilbert Scale Inclusions
I'm looking at properties of the scale of Hilbert spaces $(X_s)_{s\in \mathbb{R}}$, which are constructed as follows. Starting with $A:D(A)\subset H\to H$, $A$ a densely defined, strictly positive ($ …
- 23k
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Properties of Cameron Martin Space
In the case that I'm working with a separable Hilbert space, $H$, on which I have a trace class operator, $K$, that's coming from a Gaussian (i.e., $K$ is self-adjoint, and for simplicity, has trivial …
- 54.2k
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Da Prato's notion of Symmetric Operator
For anyone who's familiar with G. Da Prato's books on infinite dimensional analysis, I was wondering if someone could clarify something. In, for instance, "An Introduction to Infinite Dimensional Ana …
- 379