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Power Series Methods and Multisummability
Author(s) -
Balser Werner,
Braun R�diger W.
Publication year - 2000
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/(sici)1522-2616(200004)212:1<37::aid-mana37>3.0.co;2-p
Subject(s) - mathematics , series (stratigraphy) , power series , power (physics) , function series , formal power series , contrast (vision) , power function , mathematical analysis , computer science , artificial intelligence , paleontology , biology , physics , quantum mechanics
We recall the notion of a power series summability method and show, using results of W. B alser and A. B eck , that existence of a power series method which is stronger than multisummability would be equivalent to existence of an entire function with certain particular properties. We then prove that such entire functions cannot exist. In contrast to this negative result, we show that an iteration of power series methods is indeed stronger than multisummability.