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Finitely generated function algebras
The theory of function algebras has been an active field of research over the past two decades and its coming of age has been heralded by the appearance within the last twelve months of three textbooks devoted entirely to them, namely the books by Browder, Leibowitz and Gamelin. One of the attractiv...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613276852977664 |
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| access_status_str | Open Access |
| author | Sacks, Jonathan |
| author2 | Kotzé, W |
| author_browse | Kotzé, W Sacks, Jonathan |
| author_facet | Kotzé, W Sacks, Jonathan |
| author_sort | Sacks, Jonathan |
| collection | Thesis |
| description | The theory of function algebras has been an active field of research over the past two decades and its coming of age has been heralded by the appearance within the last twelve months of three textbooks devoted entirely to them, namely the books by Browder, Leibowitz and Gamelin. One of the attractive features of the theory of function algebras is that it draws on diverse specialities like the theory of Banach algebras, harmonic analysis and the theory of analytic functions of several complex variables. The last mentioned theory has led to some of the most powerful results in the theory of function algebras. Not surprisingly, many of these results, for example Rossi's local maximum modulus principle theorem 2.24, were first proved for finitely generated and then extended to arbitrary function algebras. This observation, together with the fact that there has been no systematic study of finitely generated function algebras, led to the writing of this thesis. We have made use of some of the results of the theory of analytic functions of several complex variables, though we have not specifically used the methods thereof. What we have looked for is ways in which the functions of finitely generated function algebras behave like analytic functions and then tried to see if arbitrarily generated function algebras behave in a similar way. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/18037 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:33:33.643Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| 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:11427/18037 Finitely generated function algebras Sacks, Jonathan Kotzé, W Mathematics Function Algebras The theory of function algebras has been an active field of research over the past two decades and its coming of age has been heralded by the appearance within the last twelve months of three textbooks devoted entirely to them, namely the books by Browder, Leibowitz and Gamelin. One of the attractive features of the theory of function algebras is that it draws on diverse specialities like the theory of Banach algebras, harmonic analysis and the theory of analytic functions of several complex variables. The last mentioned theory has led to some of the most powerful results in the theory of function algebras. Not surprisingly, many of these results, for example Rossi's local maximum modulus principle theorem 2.24, were first proved for finitely generated and then extended to arbitrary function algebras. This observation, together with the fact that there has been no systematic study of finitely generated function algebras, led to the writing of this thesis. We have made use of some of the results of the theory of analytic functions of several complex variables, though we have not specifically used the methods thereof. What we have looked for is ways in which the functions of finitely generated function algebras behave like analytic functions and then tried to see if arbitrarily generated function algebras behave in a similar way. 2016-03-21T19:06:03Z 2016-03-21T19:06:03Z 1970 Master Thesis Masters MSc http://hdl.handle.net/11427/18037 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics Function Algebras Sacks, Jonathan Finitely generated function algebras |
| thesis_degree_str | Master's |
| title | Finitely generated function algebras |
| title_full | Finitely generated function algebras |
| title_fullStr | Finitely generated function algebras |
| title_full_unstemmed | Finitely generated function algebras |
| title_short | Finitely generated function algebras |
| title_sort | finitely generated function algebras |
| topic | Mathematics Function Algebras |
| url | http://hdl.handle.net/11427/18037 |
| work_keys_str_mv | AT sacksjonathan finitelygeneratedfunctionalgebras |