Integration in Hermite spaces of analytic functions

Abstract

We study integration in a class of Hilbert spaces of analytic functions defined on the Rs. The functions are characterized by the property that their Hermite coefficients decay exponentially fast. We use Gauss–Hermite integration rules and show that the errors of our algorithms decay exponentially fast. Furthermore, we study tractability in terms of s and logε−1 and give necessary and sufficient conditions under which we achieve exponential convergence with EC-weak, EC-polynomial, and EC-strong polynomial tractability.