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Inverse nodal problems on quantum tree graphs

Published online by Cambridge University Press:  16 December 2021

Chuan-Fu Yang
Affiliation:
Department of Applied Mathematics, School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, People's Republic of China (chuanfuyang@njust.edu.cn, daiquanliu@njust.edu.cn)
Dai-Quan Liu
Affiliation:
Department of Applied Mathematics, School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, People's Republic of China (chuanfuyang@njust.edu.cn, daiquanliu@njust.edu.cn)

Abstract

We consider inverse nodal problems for the Sturm–Liouville operators on the tree graphs. Can only dense nodes distinguish the tree graphs? In this paper it is shown that the data of dense-nodes uniquely determines the potential (up to a constant) on the tree graphs. This provides interesting results for an open question implied in the paper.

Type
Research Article
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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