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memoria.pdf (270.48 KB)

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Bachelor thesis

Publication date

2016-06-26

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cc-by-nc-nd (c) Gabriel García Arenas, 2016
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/108830

Tools of differential calculus to solve funcional equations

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Abstract

In this work we first prove the converse of Taylor’s Theorem. This allows us to prove next the Omega-lemma and the differentiability of the Evaluation map for certain Banach spaces of analytic functions. These two theorems together with the Implicit Function Theorem are applied to certain functional equations in order to prove Poincaré’s Linearization Theorem and the Analytic Stable Manifold Theorem.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: Ernest Fontich

Subject

Equacions funcionals, Treballs de fi de grau, Espais de Banach, Funcions analítiques, Anàlisi global (Matemàtica), Espais vectorials normats

Subject (English)

Functional equations, Bachelor's theses, Banach spaces, Analytic functions, Global analysis (Mathematics), Normed linear spaces

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

GARCÍA ARENAS, Gabriel. Tools of differential calculus to solve funcional equations. [consulted: 8 of August of 2026]. Available at: https://hdl.handle.net/2445/108830

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