On Bourgain's counterexample for the Schrödinger maximal function
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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2019
- DOI:
- 10.48550/arXiv.1912.10574
- arXiv:
- arXiv:1912.10574
- Bibcode:
- 2019arXiv191210574P
- Keywords:
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- Mathematics - Classical Analysis and ODEs
- E-Print:
- 28 pages, fixes a couple typos