© 2011

Convolution Operators on Groups


Part of the Lecture Notes of the Unione Matematica Italiana book series (UMILN, volume 11)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Antoine Derighetti
    Pages 1-23
  3. Antoine Derighetti
    Pages 25-32
  4. Antoine Derighetti
    Pages 33-44
  5. Antoine Derighetti
    Pages 45-64
  6. Antoine Derighetti
    Pages 65-84
  7. Antoine Derighetti
    Pages 85-99
  8. Antoine Derighetti
    Pages 101-144
  9. Antoine Derighetti
    Pages 145-160
  10. Back Matter
    Pages 161-171

About this book


This volume is devoted to a systematic study of the Banach algebra of the convolution operators of a locally compact group. Inspired by classical Fourier analysis we consider operators on Lp spaces, arriving at a description of these operators and Lp versions of the theorems of Wiener and Kaplansky-Helson.


22DXX; 43A10; 43A20; 43A22; 43A40; 43A45; 43A15 Amenable groups Convolution operator

Authors and affiliations

  1. 1.EPFL SB-DO, MA A1 354 (Bâtiment MA) Station 8Ecole polytechnique fédérale de LausanneLausanneSwitzerland

Bibliographic information

  • Book Title Convolution Operators on Groups
  • Authors Antoine Derighetti
  • Series Title Lecture Notes of the Unione Matematica Italiana
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-642-20655-9
  • eBook ISBN 978-3-642-20656-6
  • Series ISSN 1862-9113
  • Edition Number 1
  • Number of Pages XII, 171
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Abstract Harmonic Analysis
  • Buy this book on publisher's site


From the reviews:

“This is a useful, self-contained introduction to the Banach algebra of convolution operators on a locally compact group G … . It is the first book dedicated to this topic, gathering results mainly due to Herz and, among others, to Lohoué and the author of the book. Many references on related topics are given in the notes.” (Françoise Lust-Piquard, Mathematical Reviews, Issue 2012 e)