Georgi Raikov (Pontificia Universidad Católica de Chile, Santiago)
Local Eigenvalue Asymptotics of the Perturbed Krein Laplacian
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).