Spectral theory of discontinuous functions of self-adjoint operators: essential spectrum
classification
🧮 math.SP
math.FA
keywords
varphiessentialfunctionsoperatorsscatteringself-adjointspectrumtheory
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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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