Department of Mathematics

Prof. Joris Roos, University of Wisconsin-Madison: "Discrete analogues of maximally modulated oscillatory integrals of Stein-Wainger type"

Jul 05, 2019 from 10:15 AM to 11:15 AM

LMS 4 - Raum 312 - Diskussionsraum


In 2001, Stein and Wainger introduced an interesting class of maximally modulated oscillatory integral operators related to Carleson's theorem. This talk is about the L2 theory for discrete analogues of some of these operators. This problem features a number of new and substantial difficulties arising from a curious fusion of number theory and analysis. Our approach is building on work of Krause (2018) and Krause-Lacey (2015). A key ingredient for the proof is a certain multi-frequency L2 estimate that also seems interesting in its own right. We will discuss a classical argument of Bourgain that allows us to obtain such an inequality by making use of variation-norm estimates. The required variation-norm estimates in this context were established recently in work of Guo-Roos-Yung (2017).


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