Math @ Duke

Publications [#354950] of Lillian B. Pierce
Papers Published
 Pierce, LB, ON BOURGAIN’S COUNTEREXAMPLE for the SCHRÖDINGER MAXIMAL FUNCTION,
The Quarterly Journal of Mathematics, vol. 71 no. 4
(December, 2020),
pp. 13091344, Oxford University Press (OUP) [doi]
(last updated on 2021/04/20)
Abstract: This paper provides a rigorous derivation of a counterexample of Bourgain, related to a wellknown 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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