To the spectral theory of vector-valued Sturm–Liouville operators with summable potentials and point interactions
Yaroslav GranovskyiNational Academy of Science of Ukraine, Slavyansk, Ukraine
Mark M. MalamudNational Academy of Science of Ukraine, Slavyansk, Ukraine
Hagen NeidhardtKarl-Weierstraß-Institut für Mathematik, Berlin, Germany
Andrea PosilicanoUniversità dell'Insubria, Como, Italy
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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.