## Prof. Dr. Matthias Keller

### Project leader

Universität Potsdam

E-mail: mkeller(at)math.uni-potsdam.de

Telephone: +49 331 977-2259

Homepage: https://www.math.uni-potsdam.de/professu...

## Publications within SPP2026

Given two weighted graphs $(X,b_k,m_k)$, $k=1,2$ with $b_1\sim b_2$ and $m_1\sim m_2$, we prove a weighted $L^1$-criterion for the existence and completeness of the wave operators $W_{\pm}(H_{2},H_1, I_{1,2})$, where $H_k$ denotes the natural Laplacian in $\ell^2(X,m_k)$ w.r.t. $(X,b_k,m_k)$ and $I_{1,2}$ the trivial identification of $\ell^2(X,m_1)$ with $\ell^2(X,m_2)$. In particular, this entails a general criterion for the absolutely continuous spectra of $H_1$ and $H_2$ to be equal.

Journal | Math. Phys. Anal. Geom. |

Pages | 21-28 |

Link to preprint version |

**Related project(s):****19**Boundaries, Greens formulae and harmonic functions for graphs and Dirichlet spaces

We study the Kazdan-Warner equation on canonically compactifiable graphs. These graphs are distinguished as analytic properties of Laplacians on these graphs carry a strong resemblance to Laplacians on open pre-compact manifolds.

**Related project(s):****19**Boundaries, Greens formulae and harmonic functions for graphs and Dirichlet spaces