Abstract
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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Pushnitski, A. Spectral Theory of Discontinuous Functions of Self-Adjoint Operators: Essential Spectrum. Integr. Equ. Oper. Theory 68, 75–99 (2010). https://doi.org/10.1007/s00020-010-1789-4
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DOI: https://doi.org/10.1007/s00020-010-1789-4