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A note on pointwise convergence for the Schrödinger equation

Published online by Cambridge University Press:  06 November 2017

RENATO LUCÀ  and
KEITH M. ROGERS
RENATO LUCÀ
Affiliation:
Departement Matematik und Informatik, Speigelgacse, Universität Basel, 4051, Switzerland. e-mail: renato.luca@unibas.ch
KEITH M. ROGERS
Affiliation:
Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Calle Nicolás Cabrera 13-15, Madrid, 28049, Spain. e-mail: keith.rogers@icmat.es
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Abstract

We consider Carleson's problem regarding pointwise convergence for the Schrödinger equation. Bourgain proved that there is initial data, in Hs(ℝn) with $s<\frac{n}{2(n+1)}$, for which the solution diverges on a set of nonzero Lebesgue measure. We provide a different example enabling the generalisation to fractional Hausdorff measure.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 166 , Issue 2 , March 2019 , pp. 209 - 218
Copyright
Copyright © Cambridge Philosophical Society 2017 

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