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Results tagged with fa.functional-analysis
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user 68927
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
7
votes
1
answer
728
views
Feynman-Kac formula for the GFF
The Feynman-Kac formula says that $$ \exp(-t(-\Delta+V(X)))(x,y) = \mathbb{E}_{\gamma(0)=x,\gamma(t)=y}\left[\exp(-\int_0^t V\circ\gamma)\right] $$ where $\Delta$ is the Laplacian on $L^2(\mathbb{R}^n …
- 396
2
votes
1
answer
363
views
Characterization of absolutely-continuous spectrum
The essential spectrum of a bounded linear operator $A$ on a separable Hilbert space $\mathcal{H}$ is defined as $$ \sigma_{\mathrm{ess}}(A) \equiv\left\{z\in\mathbb{C}\left.\right|A-z\mathbb{1}\text{ …
- 396