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On the Properties of Gevreyand Ultra-analytic Spaces
Linnaeus University, Faculty of Technology, Department of Mathematics.
2016 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

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.

Place, publisher, year, edition, pages
2016.
Keyword [en]
Analysis, Gevrey Regularity, Ultra-analytic functions
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:lnu:diva-55596OAI: oai:DiVA.org:lnu-55596DiVA: diva2:952969
Subject / course
Mathematics
Educational program
Applied Mahtematics Programme, 180 credits
Supervisors
Examiners
Available from: 2016-08-16 Created: 2016-08-16 Last updated: 2016-08-16Bibliographically approved

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