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
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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
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