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On Slow Decrease
Author(s) -
Goldie Charles M.,
Trustrum G. B.
Publication year - 1980
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/s2-22.3.486
Subject(s) - counterexample , sequence (biology) , oscillation (cell signaling) , statement (logic) , mathematics , combinatorics , pure mathematics , chemistry , philosophy , linguistics , biochemistry
In 1925 R. Schmidt stated that every slowly decreasing sequence may be expressed as the sum of a slowly oscillating sequence and a non‐decreasing sequence. We give a counterexample. A similar statement about slowly decreasing functions, made by Wiener in 1930, is also incorrect. However, such decompositions are known to be available if the slow‐decrease and slow‐oscillation conditions are suitably strengthened or weakened together.