Perturbation Theory for Pseudo Lapacians
Number Theory
2023-03-21 v1 Functional Analysis
Abstract
We generalise the notion of the Pseudo-Laplacian on a hyperbolic Riemann surface with one cusp, that was studied by Lax and Phillips and Colin de Verdi\`ere, by considering a boundary condition of Robin type for the constant term instead of the classical Dirichlet condition. The resulting family of Pseudo-Laplacians is a holomorphic family of unbounded operators in the sense of Kato. By use of holomorphic perturbation theory, we study the eigenvalues and eigenvectors of this family and give a new proof for the meromorphic continuation of the Eisenstein series.
Cite
@article{arxiv.2303.10424,
title = {Perturbation Theory for Pseudo Lapacians},
author = {Marlis Balkenhol},
journal= {arXiv preprint arXiv:2303.10424},
year = {2023}
}
Comments
This is a preprint. It has not yet been peer-reviewed or accepted for publication, and does not contain any modifications that may be requested after submission