Spectral theory of discontinuous functions of self-adjoint operators: essential spectrum

Details Spectral theory of discontinuous functions of self-adjoint operators: essential spectrum Spectral theory of discontinuous functions of self-adjoint operators: essential spectrum

2009-07-20

arxiv.org/abs/0907.3370v1

Mathematics

Spectral Theory

Latex, 25 pages

Scientific paper

Let $H_0$ and $H$ be self-adjoint operators in a Hilbert space. In the
scattering theory framework, we describe the essential spectrum of the
difference $\varphi(H)-\varphi(H_0)$ for piecewise continuous functions
$\varphi$. This description involves the scattering matrix for the pair $H$,
$H_0$.

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