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Generalisations of the theorem of Peter and Weyl
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 interpret...
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| Format: | Thesis |
| Language: | English English |
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Department of Mathematics and Applied Mathematics
2025
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| _version_ | 1867613284733026304 |
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| access_status_str | Open Access |
| author | Stevenson, Elizabeth |
| author2 | Russo, Francesco G |
| author_browse | Russo, Francesco G Stevenson, Elizabeth |
| author_facet | Russo, Francesco G Stevenson, Elizabeth |
| author_sort | Stevenson, Elizabeth |
| collection | Thesis |
| description | 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. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/41923 |
| institution | University of Cape Town (South Africa) |
| language | English eng |
| last_indexed | 2026-06-10T12:33:41.762Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/41923 Generalisations of the theorem of Peter and Weyl Stevenson, Elizabeth Russo, Francesco G Bavuma, Yanga analysis on general topological groups Unitary representations of locally compact groups Convergence and absolute convergence of Fourier series 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. 2025-09-30T11:22:37Z 2025-09-30T11:22:37Z 2025 2025-09-25T09:51:26Z Thesis / Dissertation Masters MSc http://hdl.handle.net/11427/41923 en eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | analysis on general topological groups Unitary representations of locally compact groups Convergence and absolute convergence of Fourier series Stevenson, Elizabeth Generalisations of the theorem of Peter and Weyl |
| thesis_degree_str | Master's |
| title | Generalisations of the theorem of Peter and Weyl |
| title_full | Generalisations of the theorem of Peter and Weyl |
| title_fullStr | Generalisations of the theorem of Peter and Weyl |
| title_full_unstemmed | Generalisations of the theorem of Peter and Weyl |
| title_short | Generalisations of the theorem of Peter and Weyl |
| title_sort | generalisations of the theorem of peter and weyl |
| topic | analysis on general topological groups Unitary representations of locally compact groups Convergence and absolute convergence of Fourier series |
| url | http://hdl.handle.net/11427/41923 |
| work_keys_str_mv | AT stevensonelizabeth generalisationsofthetheoremofpeterandweyl |