Wave envelope estimates in Fourier restriction theory

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• Dominique Maldague (University of Cambridge)
• Wednesday 20 November 2024, 13:30-15:00
• MR4, CMS.

If you have a question about this talk, please contact Julia Wolf.

Wave packet decomposition allows us to express functions with restricted frequency support as a superposition of wave packets (simpler functions which are localized in both space and frequency). A wave envelope estimate is a new type of inequality in Fourier restriction theory which provides extra information about how wave packets can combine to maximize an Lp norm. Larry Guth and I proved a version of wave envelope estimates for the cone which led to new exponential sum estimates that are relevant in number theory. In a recent paper of Xiaochun Li and Xuerui Yang, these estimates appeared as the key new tool to prove the current best known bounds for the Gauss circle problem and the Dirichlet divisor problem.

This talk is part of the Discrete Analysis Seminar series.

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