  We study multivariate approximation of periodic function in the worst case
setting with the error measured in the $L_\infty$ norm. We consider algorithms
that use standard information $\Lambda^{\rm std}$ consisting of function values
or general linear information $\Lambda^{\rm all}$ consisting of arbitrary
continuous linear functionals. We investigate the equivalences of various
notions of algebraic and exponential tractability for $\Lambda^{\rm std}$ and
$\Lambda^{\rm all}$ under the absolute or normalized error criterion, and show
that the power of $\Lambda^{\rm std}$ is the same as the one of $\Lambda^{\rm
all}$ for some notions of algebraic and exponential tractability. Our result
can be applied to weighted Korobov spaces and Korobov spaces with exponential
weight. This gives a special solution to Open problem 145 as posed by Novak and
Wo\'zniakowski (2012).
