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arXiv · 2303.10424

Perturbation Theory for Pseudo Lapacians

Marlis Balkenhol
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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.

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Marlis Balkenhol. 2023-03-18. Perturbation Theory for Pseudo Lapacians. https://arxiv.org/abs/2303.10424

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