dc.contributor.advisor | Luef, Franz | |
dc.contributor.advisor | Ortega, Eduard | |
dc.contributor.author | Austad, Are | |
dc.date.accessioned | 2021-04-23T07:23:46Z | |
dc.date.available | 2021-04-23T07:23:46Z | |
dc.date.issued | 2021 | |
dc.identifier.isbn | 978-82-326-6975-2 | |
dc.identifier.issn | 2703-8084 | |
dc.identifier.uri | https://hdl.handle.net/11250/2739232 | |
dc.description.abstract | This thesis concerns several aspects of twisted convolution algebras, with a particular focus on problems arising in Gabor analysis. A significant portion of the thesis is dedicated to the study of Hilbert C -modules known as Heisenberg modules and how they relate to Gabor frame theory. This relation showcases the link between finite Hilbert C -module frames and Gabor frames. Further, the thesis concerns certain properties of twisted convolution algebras of locally compact groups, in particular spectral invariance and C -uniqueness, and we find use for both these properties in Gabor analysis. The problem of C -uniqueness is also considered for the case of twisted convolution algebras of second-countable locally compact Hausdorff étale groupoids. | en_US |
dc.description.abstract | Sammendrag:
Denne avhandlingen omfatter flere aspekter ved tvistede konvolusjonsalgebraer, med spesielt fokus på problemer som oppstår i Gaboranalyse. En stor del av avhandlingen er dedikert til studiet av Hilbert C -moduler kjent som Heisenbergmoduler og hvordan disse relateres til teorien om Gaborrammer. Denne relasjonen viser sammenhengen mellom endelige Hilbert C -modulrammer og Gaborrammer. Videre omfatter avhandlingen enkelte egenskaper ved tvistede konvolusjonsalgebraer,
spesielt spektralinvarians ogC -entydighet, og vi finner anvendelser for begge disse konseptene i Gaboranalyse. Spørsmålet om C -entydighet blir også bektraktet for tvistede konvolusjonsalgebraer relatert til annentellbare lokalkompakte Hausdorff étalegruppoider | en_US |
dc.language.iso | eng | en_US |
dc.publisher | NTNU | en_US |
dc.relation.ispartofseries | Doctoral theses at NTNU;2021:155 | |
dc.relation.haspart | Paper A: Austad, Are; Enstad, Ulrik Bo Rufus. Heisenberg Modules as Function Spaces. Journal of Fourier Analysis and Applications 2020 ;Volum 26.(24)
https://doi.org/10.1007/s00041-020-09729-7
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) (http://creativecommons.org/licenses/by/4.0/), | en_US |
dc.relation.haspart | Paper B: Austad, Are; Jakobsen, Mads Sielemann; Luef, Franz. Gabor duality theory for Morita equivalent C*-algebras. International Journal of Mathematics 2020 ;Volum 31.(10)
https://doi.org/10.1142/S0129167X20500731
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) (http://creativecommons.org/licenses/by/4.0/), | en_US |
dc.relation.haspart | Paper C: Spectral invariance of *-representations of twisted convolution algebras with applications in Gabor analysis.
The final published version is available in Journal of Fourier Analysis and Applications.
https://doi.org/10.1007/s00041-021-09860-z
This article is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0) | en_US |
dc.relation.haspart | Paper D: Austad, Are; Ortega Esparza, Eduardo. C∗-uniqueness Results for Groupoids. International mathematics research notices 2020
https://doi.org/10.1093/imrn/rnaa225
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) (http://creativecommons.org/licenses/by/4.0/), | en_US |
dc.title | Twisted Convolution Algebras and Applications to Gabor Analysis | en_US |
dc.type | Doctoral thesis | en_US |
dc.subject.nsi | VDP::Mathematics and natural science: 400::Mathematics: 410 | en_US |