Analysis Seminar-Matthew Blair (UNM)
Event Description:
Title: Lp bounds for Schrödinger eigenfunctions
Abstract: We consider upper bounds on the growth of Lp norms of high frequency eigenfunctions of Schrödinger operators on a compact Riemannian manifold. Our treatment will begin with a review of the classical theory for Laplace operators without a potential, including the bounds of C. Sogge. We will then turn to a case of recent interest, nontrivial potentials which are nonsmooth and satisfy critical behavior with respect to scaling. The Kato class potentials will also be seen to play a crucial role in establishing the existence and regularity of these eigenfunctions. This is based on joint works with X. Huang, Y. Sire, and C. Sogge.