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Properties of the Ahlfors function

Otsetova, Anna-Mariya LU (2021) In Bachelor’s Theses in Mathematical Sciences MATK11 20211
Mathematics (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.
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author
Otsetova, Anna-Mariya LU
supervisor
organization
course
MATK11 20211
year
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}},
}