Functional Analysis and Operator Theory for Quantum Physics
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(2) National Academy of Science of Ukraine, Slavyansk, Ukraine
(3) Università dell'Insubria, Como, Italy
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.
Keywords: Vector-valued Sturm–Liouville operator, point interaction, spectrum, absolutely and singular continuous spectrum, eigenvalues, boundary triplets, Weyl function