On Bourgain's counterexample for the Schr\"odinger maximal function
Classical Analysis and ODEs
2020-11-02 v4
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 Schr\"odinger 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.
Cite
@article{arxiv.1912.10574,
title = {On Bourgain's counterexample for the Schr\"odinger maximal function},
author = {Lillian B. Pierce},
journal= {arXiv preprint arXiv:1912.10574},
year = {2020}
}
Comments
28 pages, fixes a couple typos