Journal
MATHEMATISCHE NACHRICHTEN
Volume 288, Issue 11-12, Pages 1286-1302Publisher
WILEY-V C H VERLAG GMBH
DOI: 10.1002/mana.201400277
Keywords
Colombeau algebra; set of indices; Landau big-O
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Funding
- Austrian Science Fund FWF [P25116, P25311, P23714, P25064]
- Austrian Science Fund (FWF) [P 25116, P 23714] Funding Source: researchfish
- Austrian Science Fund (FWF) [P25311, P25116, P23714] Funding Source: Austrian Science Fund (FWF)
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We define a general notion of set of indices which, using concepts from pre-ordered sets theory, permits to unify the presentation of several Colombeau-type algebras of nonlinear generalized functions. In every set of indices it is possible to generalize Landau's notion of big-O such that its usual properties continue to hold. Using this generalized notion of big-O, these algebras can be formally defined the same way as the special Colombeau algebra. Finally, we examine the scope of this formalism and show its effectiveness by applying it to the proof of the pointwise characterization in Colombeau algebras. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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