Karamata's theorem for regularised Cauchy transforms

Abstract

We prove Abelian and Tauberian theorems for regularised Cauchy transforms of positive Borel measures on the real line whose distribution functions grow at most polynomially at infinity. In particular, we relate the asymptotics of the distribution functions to the asymptotics of the regularised Cauchy transform.

Cited by in corpus (1)

• The spectral $\zeta$-function for quasi-regular Sturm--Liouville operators