BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dale Frymark (Nuclear Physics Institute CAS) DTSTART:20201124T134500Z DTEND:20201124T144500Z DTSTAMP:20260412T205341Z UID:qc_seminar/2 DESCRIPTION:Title: Singular boundary conditions for Sturm-Liouville operators via perturba tion theory\nby Dale Frymark (Nuclear Physics Institute CAS) as part o f Quantum Circle\n\n\nAbstract\nWe show that all self-adjoint extensions o f semi-bounded Sturm-Liouville operators with general limit-circle endpoin t(s) can be obtained via an additive singular form bounded self-adjoint pe rturbation of rank equal to the deficiency indices\, say d=1 or 2. This ch aracterization generalizes the well-known analog for semi-bounded Sturm-Li ouville operators with regular endpoints. Explicitly\, every self-adjoint extension of the minimal operator can be written as\n$$\n A_{\\Theta} = A_0 + B \\Theta B*\,\n$$\nwhere $A_0$ is a distinguished self-adjoint ext ension and Theta is a self-adjoint linear relation in $\\mathbb{C}^d$. The perturbation is singular in the sense that it does not belong to the unde rlying Hilbert space but is form bounded with respect to $A_0$\, i.e. it belongs to $H_{-1}(A_0)$. The construction of a boundary triple and compat ible boundary pair for the symmetric operator ensure that the perturbation is well-defined and self-adjoint extensions are in a one-to-one correspon dence with self-adjoint relations $\\Theta$.\n\nAs an example\, self-adjoi nt extensions of the classical symmetric Jacobi differential equation (whi ch has two limit-circle endpoints) are obtained and their spectra is analy zed with tools both from the theory of boundary triples and perturbation t heory.\n LOCATION:https://researchseminars.org/talk/qc_seminar/2/ END:VEVENT END:VCALENDAR