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Counterexamples for the fractal Schrödinger convergence problem with an Intermediate Space Trick
(2021-12-09)
We construct counterexamples for the fractal Schrödinger convergence problem by combining a fractal extension of Bourgain's counterexample and the intermediate space trick of Du--Kim--Wang--Zhang. We confirm that the same ...
Pointwise Convergence over Fractals for Dispersive Equations with Homogeneous Symbol
(2021-08-24)
We study the problem of pointwise convergence for equations of the type
$i\hbar\partial_tu + P(D)u = 0$, where the symbol $P$ is real, homogeneous and non-singular.
We prove that for initial data $f\in H^s(\mathbb{R}^n)$ ...
A geometric and physical study of Riemann's non-differentiable function
(2020-07-08)
Riemann's non-differentiable function is a classic example of a continuous but almost nowhere differentiable function, whose analytic regularity has been widely studied since it was proposed in the second half of the 19th ...