Oper. Matrices 2, 417-434 (2008) [DOI: 10.7153/oam-02-25]

On the Absolutely Continuous Spectrum of Sturm-Liouville Operators with Applications to Radial Quantum Trees

Michael Schmied, Robert Sims, and Gerald Teschl

We consider standard subordinacy theory for general Sturm-Liouville operators and give criteria when boundedness of solutions implies that no subordinate solutions exist. As applications, we prove a Weidmann-type result for general Sturm-Liouville operators and investigate the absolutely continuous spectrum of radially symmetric quantum trees.

MSC2000: Primary 34L05, 81Q10; Secondary 34L40, 47E05
Keywords: Sturm-Liouville operators, absolutely continuous spectrum, subordinacy, quantum graphs

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