BooksecrCollected Volumepp. 271–313

To the spectral theory of vector-valued Sturm–Liouville operators with summable potentials and point interactions

  • Yaroslav Granovskyi

    National Academy of Science of Ukraine, Slavyansk, Ukraine

  • Mark M. Malamud

    National Academy of Science of Ukraine, Slavyansk, Ukraine

  • Hagen Neidhardt

    Karl-Weierstraß-Institut für Mathematik, Berlin, Germany

  • Andrea Posilicano

    Università dell'Insubria, Como, Italy
To the spectral theory of vector-valued Sturm–Liouville operators with summable potentials and point interactions cover
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Abstract

The paper is devoted to the spectral theory of vector-valued Sturm–Liouville operators on the half-line with a summable potential and a finite number of point interactions. It is shown that the positive spectrum is purely absolutely continuous and of constant multiplicity. The negative spectrum is either finite or discrete with the only accumulation point at zero. Our approach relies on the thorough investigation of the corresponding Weyl functions and involves technique elaborated in our previous papers.