O konvergenci zaporedij holomorfnih funkcij

delo diplomskega seminarja

Mila Nedić (Author), Barbara Drinovec-Drnovšek (Mentor)

Abstract

V tem delu podrobneje proučujemo konvergenco zaporedij holomorfnih funkcij. Zanima nas, pod kakšnimi pogoji je limitna funkcija holomorfna oziroma kakšni so primeri, kjer se to ne zgodi. Primere zaporedij s slednjo lastnostjo med drugim konstruiramo s pomočjo Rungejevega izreka. Spoznamo tudi izreke, ki klasificirajo problem konvergence, posebej pa se osredotočimo na Osgoodov izrek in njegove posledice.

Keywords

matematika;holomorfne funkcije;enakomerna konvergenca;konvergenca po točkah;konvergenca po kompaktih;

Data

Language:	Slovenian
Year of publishing:	2022
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[M. Nedić]
UDC:	517.5
COBISS:	118590467
Views:	664
Downloads:	117
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	On the convergence of sequences of holomorphic functions
Secondary abstract:	In this work, we take a closer look at the problem of convergence of sequences of holomorphic functions. It is in our interest to specify the settings in which the limit function is holomorphic and provide examples in which the limit function fails to have the desired property. We construct such examples primarily with the use of Runge's theorem. We also study theorems which classify the problem of convergence with a special emphasis on Osgood's theorem and its consequences.
Secondary keywords:	mathematics;complex analytic functions;uniform convergence;pointwise convergence;convergence on compact sets;
Type (COBISS):	Final seminar paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	27 str.
ID:	16216881