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Decoupling inequalities for short generalized Dirichlet sequences

Yuqiu Fu, Larry Guth and Dominique Maldague

Vol. 16 (2023), No. 10, 2401–2464
Abstract

We study decoupling theory for functions on with Fourier transform supported in a neighborhood of short Dirichlet sequences {log n}n=N+1N+N12 , as well as sequences with similar convexity properties. We utilize the wave packet structure of functions with frequency support near an arithmetic progression.

Keywords
decoupling inequalities, wave packet decomposition, Dirichlet polynomials, convex sequences
Mathematical Subject Classification
Primary: 42A38, 42B20
Milestones
Received: 20 July 2021
Revised: 25 April 2022
Accepted: 28 May 2022
Published: 11 December 2023
Authors
Yuqiu Fu
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States
Larry Guth
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States
Dominique Maldague
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States

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