Partial inverse problems for Sturm-Liouville operators on trees

2015/09/04 by Bondarenko, Natalia, Shieh, Chung-Tsun
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1509.01534

Abstract

In this paper, inverse spectral problems for Sturm-Liouville operators on a tree (a graph without cycles) are studied. We show that if the potential on an edge is known a priori, then b - 1 spectral sets uniquely determine the potential functions on a tree with b external edges. Constructive solutions, based on the method of spectral mappings, are provided for the considered inverse problems.

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