Microlocal methods in spectral and scattering theory

Title: Obtaining improved Lp estimates for spectral clusters of decaying window width
Speaker: Melissa Tacy
Speaker Info: Northwestern University
Brief Description:
Special Note:

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
Time: 11:30am
Where: Lunt 105
Contact Person: Dean Baskin
Contact email: dbaskin@math.northwestern.edu
Contact Phone:
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