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.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:lnu-55596 |
| Date | January 2016 |
| Creators | Figueirinhas, Diogo |
| Publisher | Linnéuniversitetet, Institutionen för matematik (MA) |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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