AMBARZUMYAN-TYPE THEOREMS ON STAR GRAPHS

作者：Yang Chuan Fu^*; Pivovarchik Vyacheslav N; Huang Zhen You

来源：Operators and Matrices, 2011, 5(1): 119-131.

DOI：10.7153/oam-05-08

• Inverse spectral problem
• Dirac operator on star graphs
• Ambarzumyan theorem

The so-called Ambarzumyan theorem states that if the Neumann eigenvalues of the Sturm-Liouville operator -d(2)/dx(2) + q with an integrable real-valued potential q on [0,pi] are {n(2) : n >= 0}, then q = 0 for almost all x epsilon [0,pi]. In this work, the classical Ambarzumyan theorem is extended to star graphs with Dirac operators on its edges. We prove that if the spectrum of Dirac operator on star graphs coincides with for the unperturbed case, then the potential is identically zero.

• 出版日期2011-3
• 单位南京大学