Regularization and asymptotic expansion of certain distributions defined by divergent series (Q1902924)

Summary: The regularization of the distribution \(\sum_{n=- \infty}^\infty \delta (x- p^n)\), which gives a regularized value to the divergent series \(\sum_{n= -\infty}^\infty \varphi (p^n)\), is obtained in several spaces of test functions. The asymptotic expansion as \(\varepsilon\to 0^+\) of series of the type \(\sum_{n=0}^\infty \varphi (\varepsilon p^n)\) is also obtained.