  We study multivariate integration and approximation for functions belonging
to a weighted reproducing kernel Hilbert space based on half-period cosine
functions in the worst-case setting. The weights in the norm of the function
space depend on two sequences of real numbers and decay exponentially. As a
consequence the functions are infinitely often differentiable, and therefore it
is natural to expect exponential convergence of the worst-case error. We give
conditions on the weight sequences under which we have exponential convergence
for the integration as well as the approximation problem. Furthermore, we
investigate the dependence of the errors on the dimension by considering
various notions of tractability. We prove sufficient and necessary conditions
to achieve these tractability notions.
