Regularization and asymptotic expansion of certain distributions defined by divergent series

Abstract

The regularization of the distribution ∑n=−∞∞δ(x−pn). which gives a regularized value to the divergent series ∑n=−∞∞φ(pn) is obtained in several spaces of test functions. The asymptotic expansion as ϵ→0+of series of the type ∑n=0∞φ(ϵ pn) is also obtained.