O konvergenci zaporedij holomorfnih funkcij : delo diplomskega seminarja

Nedić, Mila (author), Drinovec-Drnovšek, Barbara (mentor)

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.

• Language: Slovenian
• Keywords: holomorfne funkcije, enakomerna konvergenca, konvergenca po to£kah, konvergenca po kompaktih
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2022
• PID: 20.500.12556/RUL-138807
• UDC: 517.5
• COBISS.SI-ID: 118590467
• Publication date in RUL: 19.08.2022

NEDIĆ, Mila, 2022, O konvergenci zaporedij holomorfnih funkcij : delo diplomskega seminarja [online]. Bachelor’s thesis. [Accessed 23 April 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=138807

Secondary language

• Language: English
• Title: On the convergence of sequences of holomorphic functions

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.

• Keywords: complex analytic functions, uniform convergence, pointwise convergence, convergence on compact sets