the three fundamental theorems in functional analysis

Abstract

A BSTRACT

This thesis treats functional analysis and its application. We study

function spaces with analytical structures, such as normed spaces, banach

spaces and Hilbert spaces. Our prime interest is in the most fundamental

theorems of functional analysis. There is Hanh-banach theorem,

uniform boundedness theorem, and closed graph theorem.

We give applications to Fourier analysis and applications on

existence of solution of differential and integration equations.