Abstract:

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, France).