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Article

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This item is available under a Creative Commons License for non-commercial use only

Disciplines

1.1 MATHMATICS

Publication Details

Integral Equations and Operator Theory 1-53

DOI 10.1007/s00020-013-2106-9

Abstract

We analyze the singular spectrum of selfadjoint operators which arise from pasting a finite number of boundary relations with a standard interface condition. A model example for this situation is a Schroedinger operator on a star-shaped graph with continuity and Kirchhoff conditions at the interior vertex. We compute the multiplicity of the singular spectrum in terms of the spectral measures of the Weyl functions associated with the single (independently considered) boundary relations. This result is a generalization and refinement of Theorem of I.S. Kac.

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