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ON BOURGAIN’S COUNTEREXAMPLE for the SCHRÖDINGER MAXIMAL FUNCTION

Publication ,  Journal Article
Pierce, LB
Published in: Quarterly Journal of Mathematics
December 1, 2020

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.

Duke Scholars

Published In

Quarterly Journal of Mathematics

DOI

EISSN

1464-3847

ISSN

0033-5606

Publication Date

December 1, 2020

Volume

71

Issue

4

Start / End Page

1309 / 1344

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Pierce, L. B. (2020). ON BOURGAIN’S COUNTEREXAMPLE for the SCHRÖDINGER MAXIMAL FUNCTION. Quarterly Journal of Mathematics, 71(4), 1309–1344. https://doi.org/10.1093/qmath/haaa032
Journal cover image

Published In

Quarterly Journal of Mathematics

DOI

EISSN

1464-3847

ISSN

0033-5606

Publication Date

December 1, 2020

Volume

71

Issue

4

Start / End Page

1309 / 1344

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics