Fundamental theorems of functional analysis and applications

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.