On Recovering Sturm–Liouville-Type Operators with Global Delay on Graphs from Two Spectra

Sergey Buterin ()
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Sergey Buterin: Department of Mathematics, Saratov State University, 410012 Saratov, Russia

Mathematics, 2023, vol. 11, issue 12, 1-12

Abstract: We suggest a new formulation of the inverse spectral problem for second-order functional-differential operators on star-shaped graphs with global delay. The latter means that the delay, which is measured in the direction of a specific boundary vertex, called the root, propagates through the internal vertex to other edges. Now, we intend to recover the potentials from the spectra of two boundary value problems on the graph with a common set of boundary conditions at all boundary vertices except the root. For simplicity, we focus on star graphs with equal edges when the delay parameter is not less than their length. Under the assumption that the common boundary conditions are of the Robin type and they are known and pairwise linearly independent, the uniqueness theorem is proven and a constructive procedure for solving the proposed inverse problem is obtained.

Keywords: functional-differential equation; constant delay; global delay; globally nonlocal operator; metric graph; quantum graph; inverse spectral problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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