Table of contents

  1. Front Matter
    Pages i-xiii
  2. Henry Helson
    Pages 1-49
  3. Henry Helson
    Pages 51-73
  4. Henry Helson
    Pages 75-105
  5. Henry Helson
    Pages 107-142
  6. Henry Helson
    Pages 143-163
  7. Henry Helson
    Pages 165-176
  8. Back Matter
    Pages 177-190

About this book


The reader is assumed to know the elementary part of complex funCtion theory, general topology, integration, and linear spaces. All the needed information is contained in a usual first-year graduate course on analysis. These prerequisites are modest but essential. To be sure there is a big gap between learning the Banach-Steinhaus theorem, for example, and applying it to a real problem. Filling that gap is one of the objectives of this book. It is a natural objective, because integration theory and functional analysis to a great extent developed in response to the problems of Fourier series! The exposition has been condensed somewhat by relegating proofs of some technical points to the problem sets. Other problems give results that are needed in subsequent sections; and many problems simply present interesting results of the subject that are not otherwise covered. Problems range in difficulty from very simple to very hard. The system of numeration is simple: Sec. 3. 2 is the second section of Chapter 3. The second section of the current chapter is Sec. 2. Formula (3. 2) is the second formula of Sec. 3, of the current chapter unless otherwise mentioned. With pleasure I record the debt to my notes from a course on Real Variables given by R. Salem in 1945. I wish to thank R. Fefferman, Y. Katznelson, and A. 6 Cairbre for sympathetic criti­ cism of the manuscript. Mr. Carl Harris of the Addison-Wesley Publishing Company has been most helpful in bringing the book to publication.


Fourier transform Maxima Morphism Natural Singular integral dynamical systems equality functions harmonic analysis homomorphism kernel learning object publishing topology

Authors and affiliations

  • Henry Helson
    • 1
  1. 1.University of CaliforniaBerkeleyUSA

Bibliographic information