In this thesis we examine properties of Gelfand-Shilov spaces Ssσ and Pilipović spaces Σsσ. These are spaces of smooth functions which, along with their Fourier transforms, decay sub-exponentially. Results for the two types of spaces relating to Fourier transforms, analyticity of functions, triviality of the spaces and short-time Fourier transforms are explored. It is determined that Σsσ is nontrivial if and only if s+σ>1, and that results for Ssσ when s+σ≥1 can generally be found to have corresponding counterparts for Σsσ when s+σ>1.
Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:lnu-105127 |
Date | January 2021 |
Creators | Petersson, Albin |
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 |
Page generated in 0.0014 seconds