On some smooth approximations on thick periodic multi-structures

Abstract

In this paper we study the approximation properties of measurable and square-integrable functions. In particular we show that any $$$L^2$$$-bounded function can be approximated in $$$L^2$$$-norm by smooth functions defined on a highly oscillating boundary of thick multi-structures in $$${\mathbb{R}}^n$$$. We derive the norm estimates for the approximating functions and study their asymptotic behaviour.