Properties of the Ahlfors function
(2021) In Bachelor’s Theses in Mathematical Sciences MATK11 20211Mathematics (Faculty of Engineering)
Mathematics (Faculty of Sciences)
- Abstract
- Extremal problems in analysis have been studied for more than a hundred years. The so called Ahlfors function is the solution to one such problem. In this thesis, we shall study several properties of this function in a most general domain. We will consider the Ahlfors function in the context of analytic capacity, and also relate it to Riemann maps of simply connected domains onto the unit disk. Our methods involve Gelfand representation of commutative Banach algebras and standard techniques from complex analysis.
- Popular Abstract (Swedish)
- Inom matematiken är det ofta viktigt och användbart att "maximizera" en derivata. Det betyder att man hittar en funktion som har den största derivatan i en punkt bland en familj av funktioner. Detta kallas för ett "extremal problem" och vi söker en lösning till detta problemet. Den finska matematikern Lars Ahlfors upptäckte en sådan lösning i 1947. I denna uppsatsen kommer vi utforska den funktionens egenskaper i en allmän definitionsmängd.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9054876
- author
- Otsetova, Anna-Mariya LU
- supervisor
- organization
- course
- MATK11 20211
- year
- 2021
- type
- M2 - Bachelor Degree
- subject
- keywords
- Complex Analysis, Function Theory, Analytic capacity, Ahlfors function, Gelfand representation
- publication/series
- Bachelor’s Theses in Mathematical Sciences
- report number
- LUNFMA-4118-2021
- ISSN
- 1654-6229
- other publication id
- 2021:K21
- language
- English
- id
- 9054876
- date added to LUP
- 2022-08-08 17:41:10
- date last changed
- 2022-08-08 17:41:10
@misc{9054876, abstract = {{Extremal problems in analysis have been studied for more than a hundred years. The so called Ahlfors function is the solution to one such problem. In this thesis, we shall study several properties of this function in a most general domain. We will consider the Ahlfors function in the context of analytic capacity, and also relate it to Riemann maps of simply connected domains onto the unit disk. Our methods involve Gelfand representation of commutative Banach algebras and standard techniques from complex analysis.}}, author = {{Otsetova, Anna-Mariya}}, issn = {{1654-6229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor’s Theses in Mathematical Sciences}}, title = {{Properties of the Ahlfors function}}, year = {{2021}}, }