Corpus ID: 209444402

On Bourgain's counterexample for the Schrödinger maximal function

  title={On Bourgain's counterexample for the Schr{\"o}dinger maximal function},
  author={L. Pierce},
  journal={arXiv: Classical Analysis and ODEs},
  • L. Pierce
  • Published 2019
  • Mathematics
  • arXiv: Classical Analysis and ODEs
  • 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 Schrodinger 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. 
    2 Citations
    Convergence over fractals for the periodic Schr\"odinger equation
    • 1
    • PDF