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Title: Kompaktnost in konvergenca v prostoru analitičnih funkcij Hedžet, Jaka (Author)Jakovac, Marko (Mentor) More about this mentor... MAG_Hedzet_Jaka_2021.pdf (466,11 KB)MD5: 29091DC2ED5DABA8AF7C9950E5F7568B Slovenian Master's thesis/paper (mb22) 2.09 - Master's Thesis FNM - Faculty of Natural Sciences and Mathematics V magistrskem delu predstavimo in preučujemo prostora zveznih in analitičnih funkcij kompleksne spremenljivke. Opazujemo nekatere značilnosti konvergence in kompaktnosti ter izpeljemo izrek o karakterizaciji normalnih množic. S pomočjo tega dokažemo nekatere pomembne izreke in prikažemo njihovo uporabo na konkretnem primeru. Za konec se lotimo še opazovanja dveh pomembnih funkcij in njune povezave ter predstavimo zelo znan nerešen problem. metrika, zveznost, konvergenca, kompaktnost, analitičnost, faktorizacija, normalne množice, funkcija gama, funkcija zeta 2021 [J. Hedžet] Maribor 515.1(043.2) 58178051 URN:SI:UM:DK:AKN7H6VV 83 13 FNM

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## Licences

License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes. 11.03.2021

## Secondary language

Language: English Compactness and convergence in the space of analytic functions In the thesis we define and study the spaces of continuous and analytic functions of complex variable. We notice some properties of convergence and compactness and implement a theorem that characterises normal sets. Using this we prove several important theorems and present their use on a specific example. We conclude by exploring the properties of two important functions and their relations and present a famous open problem. metrics, continuity, convergence, compactness, analyticalness, factorisation, normal sets, gamma function, zeta function