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Schrödinger equations: pointwise convergence to the initial data


Author: Luis Vega
Journal: Proc. Amer. Math. Soc. 102 (1988), 874-878
MSC: Primary 35J10
DOI: https://doi.org/10.1090/S0002-9939-1988-0934859-0
MathSciNet review: 934859
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Abstract: Let $ u(x,t)$ be the solution of the Schrödinger equation with initial data $ f$ in the Sobolev space $ {H^s}({{\mathbf{R}}^n})$ with $ s > \frac{1}{2}$. The a.e. convergence of $ u(x,t)$ to $ f(x)$ follows from a weighted estimate of the maximal function $ u * (x,t) = {\text{su}}{{\text{p}}_{t > 0}}\vert u(x,t)\vert$.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0934859-0
Article copyright: © Copyright 1988 American Mathematical Society

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