Preface

Summary

Some years ago I came across the need for precise information concerning the basis properties of sets of special functions, and the methods available for testing for such properties. This material proved to be rather widely scattered, so I began a collection of notes on the subject which have formed the foundations of the present little book.

I hope that the book will prove useful to graduate students of mathematics, particularly those whose research interests are developing in the direction of bases in Hilbert and Banach spaces: it could bridge the gap that exists between the scant treatment this topic usually receives in standard texts on functional analysis on the one hand, and the rather formidable specialist books such as Marti (1969) and Singer (1970) on the other. There is no harm in having some experience on the practical side of the business before aiming to become managing director!

I hope the book will appeal to workers in other scientific fields as well. An appendix has been included which lists many of the standard results, and this may help to make the book useful as a source of reference.

It is assumed that the reader's education will have included the usual first courses in real variable (including Lebesgue integration) and complex variable.