A counter example on nontangential convergence for oscillatory integrals

Details A counter example on nontangential convergence for oscillatory integrals A counter example on nontangential convergence for oscillatory integrals

2008-06-09

arxiv.org/abs/0806.1453v1

Mathematics

Analysis of PDEs

Scientific paper

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 $\phi$.

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