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Séminaire de EDP - Physique Mathématique

Local Eigenvalue Asymototics of the Perturbed Krein Laplacian

Georgi Raikov

( PUC, Chili )

Salle 2

le 24 janvier 2017 à 11:00

I will consider the Krein Laplacian on a regular bounded domain, perturbed by a real-valued multiplier V vanishing on the boundary. Assuming that V has a definite sign, I will discuss the asymptotics of the eigenvalue sequence which converges to the origin. In particular, I will show that the effective Hamiltonian that governs the main asymptotic term of this sequence, is the harmonic Toeplitz operator with symbol V, unitarily equivalent to a pseudodifferential operator on the boundary. This is a joint work with Vincent Bruneau (Bordeaux).