Generalisations of the theorem of Peter and Weyl
| dc.contributor.advisor | Russo, Francesco G | |
| dc.contributor.advisor | Bavuma, Yanga | |
| dc.contributor.author | Stevenson, Elizabeth | |
| dc.date.accessioned | 2025-09-30T11:22:37Z | |
| dc.date.available | 2025-09-30T11:22:37Z | |
| dc.date.issued | 2025 | |
| dc.date.updated | 2025-09-25T09:51:26Z | |
| dc.description.abstract | Introducing some classical concepts in the representation theory of compact groups, we study the historical background of the Fourier Theorem and how this result was used to solve the heat equation. Then we sketch the main steps of the proof of the Fourier Theorem, explaining how it can be interpreted as a special case of a more general argument, which is used in the proof of the Peter-Weyl Theorem. A comparative analysis of different arguments, which have been used to prove the Fourier Theorem and the Peter-Weyl Theorem in the literature, is illustrated in the present thesis. Therefore, we note that some arguments apply to compact connected abelian groups while others can't be applied. Inspecting the details of the proofs, we observe that the use of the Stone-Weierstrass Theorem plays a fundamental role, so we discuss the relevance of the Stone-Weiestrass Theorem in the proof of Peter-Weyl Theorem. | |
| dc.identifier.apacitation | Stevenson, E. (2025). <i>Generalisations of the theorem of Peter and Weyl</i>. (). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/41923 | en_ZA |
| dc.identifier.chicagocitation | Stevenson, Elizabeth. <i>"Generalisations of the theorem of Peter and Weyl."</i> ., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2025. http://hdl.handle.net/11427/41923 | en_ZA |
| dc.identifier.citation | Stevenson, E. 2025. Generalisations of the theorem of Peter and Weyl. . University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. http://hdl.handle.net/11427/41923 | en_ZA |
| dc.identifier.ris | TY - Thesis / Dissertation AU - Stevenson, Elizabeth AB - Introducing some classical concepts in the representation theory of compact groups, we study the historical background of the Fourier Theorem and how this result was used to solve the heat equation. Then we sketch the main steps of the proof of the Fourier Theorem, explaining how it can be interpreted as a special case of a more general argument, which is used in the proof of the Peter-Weyl Theorem. A comparative analysis of different arguments, which have been used to prove the Fourier Theorem and the Peter-Weyl Theorem in the literature, is illustrated in the present thesis. Therefore, we note that some arguments apply to compact connected abelian groups while others can't be applied. Inspecting the details of the proofs, we observe that the use of the Stone-Weierstrass Theorem plays a fundamental role, so we discuss the relevance of the Stone-Weiestrass Theorem in the proof of Peter-Weyl Theorem. DA - 2025 DB - OpenUCT DP - University of Cape Town KW - analysis on general topological groups KW - Unitary representations of locally compact groups KW - Convergence and absolute convergence of Fourier series LK - https://open.uct.ac.za PB - University of Cape Town PY - 2025 T1 - Generalisations of the theorem of Peter and Weyl TI - Generalisations of the theorem of Peter and Weyl UR - http://hdl.handle.net/11427/41923 ER - | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/11427/41923 | |
| dc.identifier.vancouvercitation | Stevenson E. Generalisations of the theorem of Peter and Weyl. []. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2025 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/41923 | en_ZA |
| dc.language.iso | en | |
| dc.language.rfc3066 | eng | |
| dc.publisher.department | Department of Mathematics and Applied Mathematics | |
| dc.publisher.faculty | Faculty of Science | |
| dc.publisher.institution | University of Cape Town | |
| dc.subject | analysis on general topological groups | |
| dc.subject | Unitary representations of locally compact groups | |
| dc.subject | Convergence and absolute convergence of Fourier series | |
| dc.title | Generalisations of the theorem of Peter and Weyl | |
| dc.type | Thesis / Dissertation | |
| dc.type.qualificationlevel | Masters | |
| dc.type.qualificationlevel | MSc |