Topics in Real and Functional Analysis

The main goal of the present book is to give students a concise introduc- tion which gets to some interesting results without much ado while using a sufficiently general approach suitable for further studies. Still I have tried to always start with some interesting special cases and then work my way up to the general theory. While this unavoidably leads to some duplications, it usually provides much better motivation and implies that the core ma- terial always comes first (while the more general results are then optional).
Moreover, this book is not written under the assumption that it will be read linearly starting with the first chapter and ending with the last. Con- sequently, I have tried to separate core and optional materials as much as possible while keeping the optional parts as independent as possible.
Furthermore, my aim is not to present an encyclopedic treatment but to provide a student with a versatile toolbox for further study. Moreover, in contradistinction to many other books, I do not have a particular direction in mind and hence I am trying to give a broad introduction which should prepare you for diverse fields such as spectral theory, partial differential equations, or probability theory. This is related to the fact that I am working in mathematical physics, an area where you never know what mathematical theory you will need next.