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We study multivariate approximation of periodic function in the worst casesetting with the error measured in the $L_\infty$ norm. We consider algorithmsthat use standard information $\Lambda^{\rm std}$ consisting of function valuesor general linear information $\Lambda^{\rm all}$ consisting of arbitrarycontinuous linear functionals. We investigate the equivalences of variousnotions of algebraic and exponential tractability for $\Lambda^{\rm std}$ and$\Lambda^{\rm all}$ under the absolute or normalized error criterion, and showthat the power of $\Lambda^{\rm std}$ is the same as the one of $\Lambda^{\rmall}$ for some notions of algebraic and exponential tractability. Our resultcan be applied to weighted Korobov spaces and Korobov spaces with exponentialweight. This gives a special solution to Open problem 145 as posed by Novak andWo\'zniakowski (2012).

On the power of standard information for tractability for $L_\infty$ approximation of periodic functions in the worst case setting