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Tauberian Theorems for General J p ‐Methods and a Characterization of Dominated Variation
Author(s) -
Kratz W.,
Stadtmüller U.
Publication year - 1989
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-39.1.145
Subject(s) - abelian and tauberian theorems , characterization (materials science) , mathematics , convergence (economics) , oscillation (cell signaling) , series (stratigraphy) , order (exchange) , variation (astronomy) , pure mathematics , physics , geology , astrophysics , chemistry , optics , paleontology , biochemistry , finance , economics , economic growth
We prove Tauberian theorems from the power series methods J p to convergence. The corresponding Tauberian conditions, which are of o o‐type, are mainly oscillation and gap conditions, which are valid for all J p ‐methods and which generalize known results for J p ‐methods with dominatedly varying partial sums { P n } of the coefficients { p k }. Moreover, we give a characterization of dominated variation in terms of certain quantities Δ n , which play an important role in our Tauberian conditions and which are related to the limitation order of the J p ‐methods.