M. Langer and H. Woracek,
Karamata's theorem for regularised Cauchy transforms,
Proc. Roy. Soc. Edinburgh Sect. A, to appear
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.