Abstract
AbstractWe consider an inverse problem for Schrödinger operators on connected equilateral graphs with standard matching conditions. We calculate the spectral determinant and prove that the asymptotic distribution of a subset of its zeros can be described by the roots of a polynomial. We verify that one of the roots is equal to the mean value of the potential and apply it to prove an Ambarzumian type result, i.e., if a specific part of the spectrum is the same as in the case of zero potential, then the potential has to be zero.
Funder
Nemzeti Kutatási Fejlesztési és Innovációs Hivatal
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
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