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Title: Zeros, interpolació i l'anell de funcions holomorfes en una regió
Author: Jansat Balları́n, Judit
Director/Tutor: Cascante, Ma. Carme (Maria Carme)
Keywords: Teoria geomètrica de funcions
Treballs de fi de grau
Funcions holomorfes
Subgrups de Sylow
Funcions meromorfes
Geometric function theory
Bachelor's theses
Holomorphic functions
Sylow subgroups
Meromorphic functions
Issue Date: 19-Jun-2021
Abstract: [en] In this work, we study the construction of holomorphic functions with prescribed zeros on a domain given by the Weierstrass zeros theorem and use this result and Mittag-Leffler's theorem to interpolate a sequence of numbers by a holomorphic function. As an application of the previous topics, we study some algebraic properties of the ring $\mathcal{H}(\Omega)$ and its ideals. In particular, we prove a Bézout identity in this ring given by Wedderburn lemma. Finally, we prove Bers' theorem, which states that if the holomorphic function rings on two domains are algebraically equivalent, then the respective domains are conformally equivalent.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Ma. Carme Cascante
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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