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 | References | Similar Articles | Additional Information

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 $u * (x,t) = {\text {su}}{{\text {p}}_{t > 0}}|u(x,t)|$.

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Article copyright:
© Copyright 1988
American Mathematical Society