Seminar on inverse spectral theory

  • Angkana Rüland
SG 3-14 MPI for Mathematics in the Sciences / University of Leipzig (Leipzig)


In this seminar, we are going to study the equation $$- y'' + qy = \lambda y \qquad 0 \le x \le 1$$ subject to the boundary data \(y(0)=y(1)=0\). It is assumed that the function \(q : [0,1] \to \mathbb{R}\) is given. The real number \(\lambda\) is called an eigenvalue, if a non-trivial solution to the above problem exists.

In this seminar, we investigate the relation between the potential \(q\) and the set of eigenvalues. For example, typical questions are: For which sets of real numbers does there exist a potential which has this given set as eigenvalues? Which potentials are isospectral, i.e. which potentials give the same eigenvalues? Which additional pieces of information are determined by the potential?

The theory is surprisingly complete with rich relations to other fields of mathematics.

Date and time info
Thursdays 09:15 - 10:45

Partial Differential Equations, Inverse Spectral Theory

Analysis I-III and ODEs is required; basic knowledge of functional analysis and PDEs is helpful

MSc students, PhD students, Postdocs

English, German if desired
01.10.18 31.01.19

Regular lectures Winter semester 2018-2019

MPI for Mathematics in the Sciences / University of Leipzig see the lecture detail pages

Katharina Matschke

MPI for Mathematics in the Sciences Contact via Mail