Robna Schwarzova lema

delo diplomskega seminarja

Abstract

V diplomskem delu bomo povedali nekaj o obnašanju holomorfnih preslikav, definiranih na zaprtem enotskem disku. Posebno pozornost bomo posvetili vrednostim odvodov holomorfnih preslikav v robnih negibnih točkah oz. točkam, ki ležijo na robu enotskega diska. Za ocenjevanje njihovih vrednosti se bomo sklicevali na posplošitve Schwarzove leme, kot je Juliajeva neenakost. V koliko uvedemo dodatne predpostavke lahko še bolj natančno ocenimo vrednosti odvodov v robnih negibnih točkah holomorfnih preslikav, kar nam lepo ponazorita robni princip maksima za holomorfne preslikave in Wolffova trditev.

Keywords

matematika;holomorfne preslikave;Schwarzova lema;Liouvillov izrek;Schwarz- Pickova lema;robni princip maksima za holomorfne preslikave;Juliajeva neenakost;Wolffova trditev;

Data

Language:	Slovenian
Year of publishing:	2019
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[U. Rac]
UDC:	517.5
COBISS:	18709337
Views:	2173
Downloads:	234
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Boundary Schwarz lemma
Secondary abstract:	In this thesis, we will say something about the behavior of holomorphic mappings defined on the closed unit disk. We will dedicate special attention to the values of the derivatives of holomorphic mappings at the boundary fixed points that lie on the boundary of the unit disk. For estimating their values we will refer to the generalization of the Schwarz Lemma, such as Julia's inequality. In so far as we introduce additional assumptions we can even more accurately estimate the values of the derivatives at fixed boundary points of holomorphic mappings, which is well illustrated by the Anti-calculus proposition for holomorphic functions and Wolff’s proposition.
Secondary keywords:	mathematics;holomorphic mappings;Schwarz lemma;Liouville theorem;Schwarz- Pick lemma;anti-calculus proposition;Julia inequality;Wolff proposition;
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:	32 str.
ID:	11202485