Schwarzova lema in njene posplošitve

delo diplomskega seminarja

Tea Štrekelj (Author), Franc Forstnerič (Mentor)

Abstract

Schwarzova lema se smatra za eno od elementarnih in najlepših lastnosti holomorfnih funkcij iz enotskega diska nazaj v enotski disk. Tudi njen dokaz uporablja zgolj osnovna sredstva. Odgovori pa nam na kratko in jedrnato vprašanje, kako hitro lahko taka funkcija narašča skozi izhodišče. Ta preprosta lema hkrati odpira številna vprašanja o možnih posplošitvah, o uporabah v drugih področjih in nenazadnje o svojem izvoru. V diplomski nalogi poskušamo razširiti njen domet in se približati spoznanju imena rože.

Keywords

matematika;holomorfne funkcije;harmonične funkcije;princip maksimuma;lastnost povprečne vrednosti;Cauchyjeva formula;Poissonova formula;Schwarzova lema;

Data

Language:	Slovenian
Year of publishing:	2018
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[T. Štrekelj]
UDC:	517.5
COBISS:	18477657
Views:	833
Downloads:	292
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	The Schwarz lemma and its generalizations
Secondary abstract:	The Schwarz lemma is considered to be one of the most elementary and beautiful properties of the holomorphic functions between unitary discs in the complex plane. To prove it one only needs to be familiar with the basic properties of holomorphic functions. It gives us an answer to a most short and simple question, namely how large can a derivative of such a function be at the origin. At the same time this simple lemma happens to bring up many intricate questions about possible generalizations, applications in other fields, and finally about its origin. In this diploma we endeavour to extend its scope and try to approach the case of the name of the rose.
Secondary keywords:	mathematics;holomorphic functions;harmonic functions;maximum principle;mean value property;Cauchy integral formula;Poisson integral formula;Schwarz lemma;
Type (COBISS):	Final seminar paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	28 str.
ID:	10961363