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O ‐Tauberian Theorems for J p ‐Methods with Rapidly Increasing Weights
Author(s) -
Kratz Werner,
Stadtmüller Ulrich
Publication year - 1990
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/s2-41.3.489
Subject(s) - class (philosophy) , abelian and tauberian theorems , mathematics , exponential function , pure mathematics , discrete mathematics , combinatorics , mathematical analysis , computer science , artificial intelligence
The main result of this paper is an O ‐Tauberian theorem for a general class of regular J p ‐methods. It is assumed merely that the weights are asymptotically interpolated by logarithmico‐exponential functions. If the weights are regularly varying the result can be derived from known results, but the theorem is new for rapidly increasing weights, which are considered here mainly. For this class of weights we use a new method of proof. Actually, this method can be applied to the whole class of weights in question also.