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arXiv · 0806.1453

A counter example on nontangential convergence for oscillatory integrals

Karoline Johansson
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Abstract

Consider the solution of the time-dependent Schr{ö}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 $-Δ_x$ is replaced by an operator $ϕ(D)$, with special conditions on $ϕ$.

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Karoline Johansson. 2008-06-09. A counter example on nontangential convergence for oscillatory integrals. https://arxiv.org/abs/0806.1453

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