Functional Analysis

This book is written to serve as a senior or beginning graduate text. Although the student should not expect to learn the value of a subject at the time that he is learning the subject itself, we have tried to give, in problems and examples, some of the applications of functional analysis. To mention only two, a proof is given of a version of the Riemann mapping theorem, as is a proof of the existence of a continuous function whose Fourier series diverges.