Department of

Mathematics


Seminar Calendar
for Harmonic Analysis and Differential Equations events the year of Thursday, January 23, 2020.

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    December 2019           January 2020          February 2020    
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
  1  2  3  4  5  6  7             1  2  3  4                      1
  8  9 10 11 12 13 14    5  6  7  8  9 10 11    2  3  4  5  6  7  8
 15 16 17 18 19 20 21   12 13 14 15 16 17 18    9 10 11 12 13 14 15
 22 23 24 25 26 27 28   19 20 21 22 23 24 25   16 17 18 19 20 21 22
 29 30 31               26 27 28 29 30 31      23 24 25 26 27 28 29
                                                                   

Tuesday, February 4, 2020

1:00 pm in 347 Altgeld Hall,Tuesday, February 4, 2020

Local smoothing estimates for Fourier Integral Operators

David Beltran (U. Wisconsin, Madison)

Abstract: The sharp fixed-time Sobolev estimates for Fourier Integral Operators (and therefore solutions to wave equations in Euclidean space or compact manifolds) were established by Seeger, Sogge and Stein in the early 90s. Shortly after, Sogge observed that a local average in time leads to a regularity improvement with respect to the sharp fixed-time estimates. Establishing variable-coefficient counterparts of the BourgainóDemeter decoupling inequalities, we improve the previous best known local smoothing estimates for FIOs. Moreover, we show that our results are sharp in both the Lebesgue and regularity exponent (up to the endpoint) in odd dimensions. This is joint work with Jonathan Hickman and Christopher D. Sogge.