A solution to an Ambarzumyan problem on trees

Kodai Mathematical Journal

Chun-Kong Law¹  Eiji Yanagida² 

[1] Department of Applied Mathematics National Sun Yat-sen University;Department of Mathematics Tokyo Institute of Technology

关键词: Complex dynamics;    skew product;    Green function;   

DOI  :  10.2996/kmj/1341401056

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(22)We consider the Neumann Sturm-Liouville problem defined on trees such that the ratios of lengths of edges are not necessarily rational. It is shown that the potential function of the Sturm-Liouville operator must be zero if the spectrum is equal to that for zero potential. This extends previous results and gives an Ambarzumyan theorem for the Neumann Sturm-Liouville problem on trees. To prove this, we compute approximated eigenvalues for zero potential by using a generalized pigeon hole argument, and make use of recursive formulas for characteristic functions.

【 授权许可】

Unknown