Finitely generated function algebras

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dc.contributor.advisorKotzé, Wen_ZA
dc.contributor.authorSacks, Jonathanen_ZA
dc.date.accessioned2016-03-21T19:06:03Z
dc.date.available2016-03-21T19:06:03Z
dc.date.issued1970en_ZA
dc.description.abstractThe 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.identifier.apacitationSacks, 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/11427/18037en_ZA
dc.identifier.chicagocitationSacks, 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/11427/18037en_ZA
dc.identifier.citationSacks, J. 1970. Finitely generated function algebras. University of Cape Town.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
dc.identifier.urihttp://hdl.handle.net/11427/18037
dc.identifier.vancouvercitationSacks 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/11427/18037en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematicsen_ZA
dc.subject.otherFunction Algebrasen_ZA
dc.titleFinitely generated function algebrasen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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