The Analysis Seminar

Spring 2014

The seminar meets Wednesdays in room LN 2205 at 3:30 p.m. There are refreshments and snacks in the Anderson Reading Room at 3:15.

The seminar is partly funded as one of Dean's Speaker Series in Harpur College (College of Arts and Sciences) at Binghamton University.

February 5th: Pierre Germain (Courant) (Cancelled due to weather)
Title: Big box limit for the 2 dimensional nonlinear Schrodinger equation.

February 26th: Nan Lu (Umass-Amherst)
Title: Small Generalized Breathers and Periodic Orbits for Klein-Gordon Equations

Abstract: In this talk, I will consider the Klein-Gordon equation and obtain a family of generalized breathers and periodic orbits. The result about breathers rigorously justify a formal result obtained by Segur and Kruskal.

May 8th: Michael Goldberg (Cincinnati)
Title: The Helmholtz equation with L^p data

Abstract: We investigate the existence of L² solutions of a Helmholtz equation (-Δ - 1)u = g for given data g ∈ L^p(Rⁿ). Vanishing of the Fourier transform of g along the unit sphere is a clear necessary condition. Typically one also assumes weighted decay of g so that its Fourier transform is differentiable near where it vanishes. In fact the weights are not required so long as g ∈ L^p(Rⁿ), p ≤ (2n+2)/(n+5). The proof is closely related to that of the Stein-Tomas restriction theorem.
This problem arises naturally when proving the non-existence of embedded resonances of a Schrödinger operator with potential V ∈ L^q(Rⁿ). Generalization to Bochner-Riesz multipliers of negative order (between -1/2 and -3/2) is also possible.