On Bourgain's counterexample for the Schrödinger maximal function

2019/12/23 by Pierce, Lillian B. · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.10574

Abstract

This paper provides a rigorous derivation of a counterexample of Bourgain, related to a well-known question of pointwise a.e. convergence for the solution of the linear Schrödinger equation, for initial data in a Sobolev space. This counterexample combines ideas from analysis and number theory, and the present paper demonstrates how to build such counterexamples from first principles, and then optimize them.

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• Sharp pointwise convergence of Schrödinger mean with complex time in higher dimensions

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