The INI has a new website!

This is a legacy webpage. Please visit the new site to ensure you are seeing up to date information.

Skip to content

AGA

Seminar

A Solution to an Ambarzumyan Problem on Trees

Law, C-K (National Sun Yat-sen)
Thursday 29 July 2010, 11:15-12.00

Seminar Room 1, Newton Institute

Abstract

The classical Ambarzumyan problem states that when the eigenvalues $\lambda_n$ of a Neumann Sturm-Liouville operator defined on $[0,\pi]$ are exactly $n^2$, then the potential function $q=0$. In 2007, Carlson and Pivovarchik showed the Ambarzumyan problem for the Neumann Sturm-Liouville operator defined on trees where the edges are in rational ratio. We shall extend their result to show that for a general tree, if the spectrum $\sigma(q)=\sigma(0)$, then $q=0$. In our proof, we develop a recursive formula for characteristic functions, together with a pigeon hole argument. This is a joint work with Eiji Yanagida of Tokyo Institute of Technology.

Presentation

[pdf ]

Video

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.

Back to top ∧