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On the Properties of Gevreyand Ultra-analytic Spaces

We look at the algebraic properties of Gevrey, analytic and ultraanalytic function spaces, namely their closure under composition, division and inversion. We show that both Gevrey and ultra-analytic spaces, G s with 1 ≤ s < ∞ and 0 < s < 1 respectively, form algebras. Closure under composition, division and inversion is shown to hold for the Gevrey case. For the ultra-analytic case we show it is not closed under composition. We also show that if a function is in G s , with 0 < s < 1 on a compact set, then it is in G s everywhere.

Identiferoai:union.ndltd.org:UPSALLA1/oai:DiVA.org:lnu-55596
Date January 2016
CreatorsFigueirinhas, Diogo
PublisherLinnéuniversitetet, Institutionen för matematik (MA)
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeStudent thesis, info:eu-repo/semantics/bachelorThesis, text
Formatapplication/pdf
Rightsinfo:eu-repo/semantics/openAccess

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