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memoria.pdf (526.86 KB)

Document type

Bachelor thesis

Publication date

2016-01-18

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cc-by-nc-nd (c) Joan Carles Bastons García, 2016
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/97663

Fundamental theorems of functional analysis and applications

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Abstract

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.

Description

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

Subject

Espais de Banach, Treballs de fi de grau, Espais funcionals, Sèries de Fourier, Física

Subject (English)

Banach spaces, Bachelor's theses, Function spaces, Fourier series, Physics

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

BASTONS GARCÍA, Joan Carles. Fundamental theorems of functional analysis and applications. [consulted: 15 of August of 2026]. Available at: https://hdl.handle.net/2445/97663

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