SEMINAIRE MERCREDI 7 JUIN 2006
11 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Peter Hislop
Mathematics Department, University of Kentucky (Lexington, USA)

Title: The Resonance Counting Function for Schrodinger Operators

Abstract: I will discuss the resonance counting function for Schr\"odinger
operators H_V with compactly-supported, L^\infty, real-, or
complex-valued potentials V, in odd dimensions d \geq 3. The resonance
counting function N_V (r) counts the number of resonances of the
Schr\"odinger operator H_V inside a disk of radius r in the complex.
It is known that this function is bounded above as N_V (r) \leq C r^d
but not much else. In joint work with T. Christiansen, we prove that
the set of such potentials for which the resonance counting function
has maximal order of growth d is generic.