Multi-interval dissipative Sturm–Liouville boundary-value problems with distributional coefficients

1Goriunov, AS
1Institute of Mathematics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2020, 7:10-16
Section: Mathematics
Language: English

The paper investigates spectral properties of multi-interval Sturm–Liouville operators with distributional coefficients. Constructive descriptions of all self-adjoint and maximal dissipative/accumulative extensions in terms of boundary conditions are given. Sufficient conditions for the resolvents of these operators to be operators of the trace class and for the systems of root functions to be complete are found. The results are new for one-interval boundary-value problems as well.

Keywords: Sturm–Liouville operator; multi-interval boundary value problems; distributional coefficients; maximal dissipative extension; completeness of root functions

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