Tauberian retrieval theory

Abstract

Karamata's Hauptsatz [11] and its corollary is the main tool for convergence recovery from Abel's necessary conditions and the control of oscillatory behavior of limiting processes. By modifying the basic discovery from [11], relaxing Abel's necessary conditions and lightening the control of oscillatory behavior an extended Tauberian theory is outlined. This theory goes beyond convergence recovery. It retrieves various kinds of moderate divergence. .