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Schrödinger equations: Pointwise convergence to the initial data. (English) Zbl 0654.42014
The author proves that the solution \(u(x,t)=\int_{R^ n}\hat f(\xi)e^{i| \xi | \quad 2t} e^{ix.\xi} d\xi\) of the Schrödinger equation \(i\partial u/\partial t=\Delta u\) converges a.e. to the initial data \(u(x,0)=f(x)\) belonging to \(H^ s(R^ n)\) with \(s>1/2\).
Reviewer: A.H.Narr

MSC:
42A45 Multipliers in one variable harmonic analysis
42B25 Maximal functions, Littlewood-Paley theory
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