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In this paper we consider the discrete Laplacian acting on 1-forms and we study its spectrum relative to the spectrum of the 0-form Laplacian. We show that the non zero spectrum can coincide for these Laplacians with the same nature. We examine the c
Externí odkaz:
http://arxiv.org/abs/2406.03788
Autor:
Anné, Colette, Takahashi, Junya
For each degree p, we construct on any closed manifold a family of Riemannian metrics, with fixed volume such that any positive eigenvalues of the rough and Hodge Laplacians acting on differential p-forms converge to zero. In particular, on the spher
Externí odkaz:
http://arxiv.org/abs/2106.12814
The notions of magnetic difference operator defined on weighted graphs or magnetic exterior derivative are discrete analogues of the notionof covariant derivative on sections of a fibre bundle and its extension on differential forms. In this paper, w
Externí odkaz:
http://arxiv.org/abs/2105.10171
We consider a non self-adjoint Laplacian on a directed graph with non symmetric weights on edges. We give a criterion for the m-accretiveness and the m-sectoriality of this Laplacian. Our results are based on a comparison of this operator with its sy
Externí odkaz:
http://arxiv.org/abs/1906.07596
Autor:
Anné, Colette, Post, Olaf
Since the publication of the important work of Rauch and Taylor (Potential and scattering theory on wildly perturbed domains, JFA, 1975) a lot has been done to analyse wild perturbations of the Laplace operator. Here we present results concerning the
Externí odkaz:
http://arxiv.org/abs/1802.01124
We consider a non self-adjoint Laplacian on a directed graph with non symmetric edge weights. We give necessary conditions for this Laplacian to be sectorial. We introduce a special self-adjoint operator and compare its essential spectrum with that o
Externí odkaz:
http://arxiv.org/abs/1801.01661
Autor:
Anné, Colette
Les premiers travaux que je présente ici developpent des méthodes asymptotiques qui permettent d'étudier une “continuité du spectre” pour l'opérateur de Laplace agissant sur les fonctions ou les formes différentielles d'une variété compac
Externí odkaz:
http://tel.archives-ouvertes.fr/tel-00139988
http://tel.archives-ouvertes.fr/docs/00/13/99/88/PDF/hab1.pdf
http://tel.archives-ouvertes.fr/docs/00/13/99/88/PDF/hab1.pdf
Publikováno v:
In Indagationes Mathematicae March 2020 31(2):277-293
Autor:
Anné, Colette, Torki-Hamza, Nabila
We propose a general condition, to ensure essential self-adjointness for the Gau{\ss}-Bonnet operator, based on a notion of completeness as Chernoff. This gives essential self-adjointness of the Laplace operator both for functions or 1-forms on infin
Externí odkaz:
http://arxiv.org/abs/1301.0739
Autor:
Anné, Colette, Takahashi, Junya
Publikováno v:
Anal. PDE 8 (2015) 1025-1050
The goal of the present paper is to calculate the limit spectrum of the Hodge-de Rham operator under the perturbation of collapsing one part of a manifold obtained by gluing together two manifolds with the same boundary. It appears to take place in t
Externí odkaz:
http://arxiv.org/abs/1007.2949