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Publications [#354950] of Lillian B. Pierce

Papers Published

  1. Pierce, LB, ON BOURGAIN’S COUNTEREXAMPLE for the SCHRÖDINGER MAXIMAL FUNCTION, The Quarterly Journal of Mathematics, vol. 71 no. 4 (December, 2020), pp. 1309-1344, 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 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.

 

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