Abstract
with radius of convergence 1, we wish to study the relations between the sequence (s) and its associated function f(z) which may be considered as a transformation T(s). Direct (or Abelian) theorems conclude from the sequence (s) to the transformation T(s), while Tauberian theorems infer conclusions from the behavior of T(s) to the behavior of (s) under specified additional conditions (Tauberian conditions). For the special transformation T which transforms (s) into f(z) according to (1.1) we distinguish two types of Tauberian theorems. Tauberian theorems of real character use assumptions about f(z) where z is on the real axis, and have real Tauberian conditions; for example
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call