Magda Khalile

### Eigenvalues of a Robin Laplacian on infinite sectors

Abstract: We consider the Laplacian with a Robin boundary condition on infinite sectors. The aim is to study the spectral properties of this operator, and more precisely the behavior of its eigenvalues with respect to the angle of aperture of the sector. The essential spectrum of this Robin Laplacian does not depend on the angle and the discrete spectrum is non-empty iff the aperture is less than \pi. In this case, we show that the discrete spectrum is finite and we study the behavior of the discrete eigenvalues as the angle tends to 0. In addition, we can prove a property of localization for the associated eigenfunctions which will be useful to study the Robin Laplacian on polygons.