The Gleason problem has been proven to be a complicated issue to tackle. In this thesiswe will conclude that a domain, Ω ⊂ R𝑛, has Gleason 𝑅-property at any point 𝑝 ∈ Ω, where 𝑅(Ω) ⊂ 𝐶∞(Ω) is the ring of functions that are real analytic in 𝑝. First, we investigate function spaces and give them fitting norms. Afterwards, we build a bump function that is then used to construct a smooth partition of unity on R𝑛. Finally, we show that some of the functionspaces, introduced earlier, have the Gleason property. Ultimately, we use our smooth partition of unity in order to prove that the statement above holds for domains in R2. Subsequently, with the same reasoning one can prove that the statement also holds for domains Ω ⊂ R𝑛.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:mdh-63542 |
| Date | January 2023 |
| Creators | Adlerteg, Amalia |
| Publisher | Mälardalens universitet, Akademin för utbildning, kultur och kommunikation |
| 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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