A counter example on nontangential convergence for oscillatory integrals

Karoline Johansson

A counter example on nontangential convergence for oscillatory integrals

Analysis of PDEs 2008-06-10 v1

Authors: Karoline Johansson

Abstract

Consider the solution of the time-dependent Schr{\"o}dinger equation with initial data $f$ . It is shown in \cite{artikel} that there exists $f$ in the Sobolev space $H^s(\RR), s=n/2$ such that tangential convergence can not be widened to convergence regions. In this paper we show that the corresponding result holds when $-\Delta_x$ is replaced by an operator $\phi(D)$ , with special conditions on $\phi$ .

Keywords

schrödinger equation

Cite

@article{arxiv.0806.1453,
  title  = {A counter example on nontangential convergence for oscillatory integrals},
  author = {Karoline Johansson},
  journal= {arXiv preprint arXiv:0806.1453},
  year   = {2008}
}

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