On Inverse Spectral Problems for Sturm–Liouville Differential Operators on Closed Sets

We study Sturm–Liouville operators on closed sets of a special structure, which are sometimes referred to as time scales and often appear in modelling various real-world processes. Depending on the set structure, such operators unify both differential and difference operators. The time scales under...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2021-06, Vol.42 (6), p.1201-1209
Main Authors: Kuznetsova, M. A., Buterin, S. A., Yurko, V. A.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Boundary conditions
Boundary value problems
Differential equations
Finite differences
Geometry
Inverse problems
Liouville equations
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Operators (mathematics)
Probability Theory and Stochastic Processes
Spectra
Time
Uniqueness theorems
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Summary:We study Sturm–Liouville operators on closed sets of a special structure, which are sometimes referred to as time scales and often appear in modelling various real-world processes. Depending on the set structure, such operators unify both differential and difference operators. The time scales under consideration consist of a finite number of non-intersecting segments. We obtain properties of the spectral characteristics and prove uniqueness theorems for inverse problems of recovering the operator from two types of spectral data: the Weyl function, as well as the spectra of two boundary value problems for one and the same Sturm–Liouville equation on the time scale with one common boundary condition.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080221060160