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Maximal operator estimates for the Schrödinger equation

Let $a>0$ and consider the operator $$Tf(t,x)= \int_{\mathbb{R}^{n}}e^{ i x\cdot \xi} e^{i t \lvert\xi\rvert^{a}} \widehat{f}(\xi) \, d\xi.$$ When $a=2$, the function $Tf$ solves the Cauchy problem as …
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