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

Alexander Pushnitski

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

Spectral Theory 2009-07-21 v1 Functional Analysis

Authors: Alexander Pushnitski

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 $H$ , $H_0$ .

Keywords

self-adjoint operators essential spectrum scattering theory piecewise continuous functions scattering matrix

Cite

@article{arxiv.0907.3370,
  title  = {Spectral theory of discontinuous functions of self-adjoint operators: essential spectrum},
  author = {Alexander Pushnitski},
  journal= {arXiv preprint arXiv:0907.3370},
  year   = {2009}
}

Comments

Latex, 25 pages

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