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Fundamental theorems of functional analysis and applications

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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: María Jesús Carro Rossell

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Among the fundamental theorems of Functional Analysis are the open mapping theorem, the closed graph theorem, the uniform boundedness principle, the Banach-Steinhaus theorem and the Hahn-Banach theorem. We study them in the context of Banach spaces and applications in Analysis like the divergence of Fourier series, the Riesz representation theorem, the existence of nowhere differentiable continuous functions, etc.
Apart from Mathematics, we demonstrate that those theorems can play an important role in Physics by examining two more applications: the moment problem and a rocket ascent. The whole thesis outlines that those theorems are applied in many disciplines and can lead to relevant results.

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cc-by-nc-nd (c) Joan Carles Bastons García, 2016

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Treballs Finals de Grau (TFG) - Matemàtiques

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Fundamental theorems of functional analysis and applications