Title: Obtaining improved Lp estimates for spectral clusters of decaying window width
Speaker: Melissa Tacy
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:
In many cases geometric information can be used to improve the general multiplicity eigenfunction bounds. For example Bérard obtained a log improvement in the case of negative curvature. He obtained his estimates by studying spectral cluster operators whose window width decayed as 1/logλ. Such improvements immediately imply improvements to L∞ eigenfunction bounds. In this talk I will discuss extending these improvement to Lp bounds for p<∞. Standard interpolation techniques fail to provide estimates at the kink point (the value of p that marks a regime change for sharp examples). I will present a new technique based on directional orthogonality for attacking these kind of problems.Date: Sunday, October 30, 2011