Functional Analysis and Operator Theory for Quantum Physics


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pp: 271–313

DOI: 10.4171/175-1/15

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

Yaroslav Granovskyi[1], Mark M. Malamud[2], Hagen Neidhardt and Andrea Posilicano[3]

(1) National Academy of Science of Ukraine, Slavyansk, Ukraine
(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

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