On the singular continuous spectrum of self-adjoint extensions
Copyright policy )On the singular continuous spectrum of self-adjoint extensions
Let \(H\) be a closed symmetric operator in the Hilbert space \({\mathcal H}\) with gap \(J\) and infinite deficiency indices. Given any open subset \(J_0\) of \(J\) we shall give explicitly a selfadjoint extension \(\widetilde {H}\) of \(H\) such that up to some discrete spectrum the spectrum of \(\widetilde {H}\) within the gap \(J\) of \(H\) is purely singular continuous and the singular continuous spectrum of \(\widetilde {H}\) within \(J\) equals the closure of \(J_0\) in \(J\).
- DigiZeitschriften Germany
- Bielefeld University Germany
- University of Potsdam Germany
Linear symmetric and selfadjoint operators (unbounded), extension theory, 510.mathematics, singular continuous spectrum, Institut für Mathematik, Dilations, extensions, compressions of linear operators, symmetric operator, Article, spectrum
Linear symmetric and selfadjoint operators (unbounded), extension theory, 510.mathematics, singular continuous spectrum, Institut für Mathematik, Dilations, extensions, compressions of linear operators, symmetric operator, Article, spectrum
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