4
votes
1answer
426 views

Is there a continuous function $f$ satisfying the following Zygmund condition but not differentiable.

Suppose that a continuous function $f$ on the line and satisfies $$ |f(x+2h)−2f(x+h)+f(x)|\leq const \frac{|h|}{(\log\frac{1}{|h|})^{\beta}}\,\,\,\,\,\,\text{where}\,\,\,\, \beta \in(0, 1] $$ ...
2
votes
1answer
337 views

Regularization of Zygmund functions

Dear community. I would like to derive a "good" estimate on $\frac{d}{dt}f_\epsilon(t)$, where $f_\epsilon$ is a regularization of a Zygmund-continuous function $f$, i.e. ...
4
votes
1answer
285 views

Schrodinger's equation over a randomized grid

I am interested in solutions to $$ \frac{d}{dt} \Psi = -iH \Psi $$ for $H$ hermitian and time independent. This boils down to evaluating $$ \Psi(t) = e^{-iHt}\Psi_0 $$ at points of interest $t_n$. I ...