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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
##### Keywords:
Schrödinger equation
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