Finitely generated function algebras

 

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dc.contributor.advisor Kotzé, W en_ZA
dc.contributor.author Sacks, Jonathan en_ZA
dc.date.accessioned 2016-03-21T19:06:03Z
dc.date.available 2016-03-21T19:06:03Z
dc.date.issued 1970 en_ZA
dc.identifier.citation Sacks, J. 1970. Finitely generated function algebras. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/18037
dc.description.abstract 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. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Mathematics en_ZA
dc.subject.other Function Algebras en_ZA
dc.title Finitely generated function algebras en_ZA
dc.type Master Thesis
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Science en_ZA
dc.publisher.department Department of Mathematics and Applied Mathematics en_ZA
dc.type.qualificationlevel Masters
dc.type.qualificationname MSc en_ZA
uct.type.filetype Text
uct.type.filetype Image
dc.identifier.apacitation Sacks, J. (1970). <i>Finitely generated function algebras</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/18037 en_ZA
dc.identifier.chicagocitation Sacks, Jonathan. <i>"Finitely generated function algebras."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1970. http://hdl.handle.net/11427/18037 en_ZA
dc.identifier.vancouvercitation Sacks J. Finitely generated function algebras. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1970 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/18037 en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Sacks, Jonathan AB - 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. DA - 1970 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1970 T1 - Finitely generated function algebras TI - Finitely generated function algebras UR - http://hdl.handle.net/11427/18037 ER - en_ZA


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