Spectre du Laplacien singulier associé aux métriques canoniques sur ${\mathbb{P}}^1$

Abstract

We construct a singular differential operator attached to a class of singular metrics on the line bundles over the complex projective space, ${\mathbb{P}}^1$. This operator extends the classical notion of the generalized Laplacian. We prove that this operator admits a infinite, discrete and positive spectrum. We compute it explicitly.

in French, Accepted for publication in "Journal de Mathématiques Pures et Appliquées"

References in corpus (2)

• Sur la fonction Zêta associée au Laplacien singulier ${\Delta }_{{\mathcal{O}(m)}_{\infty }}$
• The spectral theory of generalized Laplacians associated to integrable metrics on compact Riemann surfaces