On Properties of the Sturm-Liouville Operator with Degenerate Boundary Conditions
Alexander Makin
TL;DR
This paper investigates the spectral properties of the Sturm-Liouville operator with complex potential and degenerate boundary conditions, addressing inverse problems and the basis properties of root functions.
Contribution
It provides new results on inverse spectral problems and the completeness and basis properties of eigenfunctions for this class of operators.
Findings
Solved the inverse spectral problem for the operator.
Established conditions for completeness of root functions.
Analyzed basis properties of the eigenfunction system.
Abstract
We consider spectral problems for the Sturm-Liouville operator with arbitrary complex-valued potential q(x) and degenerate boundary conditions. We solve corresponding inverse problem, and also study the completeness property and the basis property of the root function system.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Numerical methods in inverse problems · Differential Equations and Boundary Problems