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Title: Tools of differential calculus to solve funcional equations
Author: García Arenas, Gabriel
Director: Fontich, Ernest, 1955-
Keywords: Equacions funcionals
Treballs de fi de grau
Espais de Banach
Funcions analítiques
Anàlisi global (Matemàtica)
Espais vectorials normats
Functional equations
Bachelor's thesis
Banach spaces
Analytic functions
Global analysis (Mathematics)
Normed linear spaces
Issue Date: 26-Jun-2016
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.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: Ernest Fontich
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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