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Absolute continuity of DOS measure for Schrödinger operators
Kotani theory gives roughly that for ergodic operators there is a certain equivalence between absolutely continuous spectrum and an absolutely continuous density of states measure.
I would like to ...
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3
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1
answer
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Restrictions on spectral measure
Given any Borel measure $\mu$ on $\mathbb{R}$, define a map that sends any $f\in C_c(\mathbb{R})$ to $$T_\mu(f)(y)=\int \langle\exp(-i x \lambda),f(x)\rangle\exp(iy\lambda)d\mu(\lambda).$$
Here $\...
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