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

2009/07/20 by Pushnitski, Alexander
#35P25 #47A40 #47B25 #47F05 #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.0907.3370

Abstract

Let H₀ and H be self-adjoint operators in a Hilbert space. In the scattering theory framework, we describe the essential spectrum of the difference φ(H)-φ(H₀) for piecewise continuous functions φ. This description involves the scattering matrix for the pair H, H₀.

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