Convolution Operators on Groups

1. Front Matter

   Pages i-xii

   PDF

2. Elementary Results

   • Antoine Derighetti

   Pages 1-23

3. The Commutation’s Theorem

   • Antoine Derighetti

   Pages 25-32

4. The Figa–Talamanca Herz Algebra

   • Antoine Derighetti

   Pages 33-44

5. The Dual of Ap(G)

   • Antoine Derighetti

   Pages 45-64

6. CV _p (G) as a Module on A _p (G)

   • Antoine Derighetti

   Pages 65-84

7. The Support of a Convolution Operator

   • Antoine Derighetti

   Pages 85-99

8. Convolution Operators Supported by Subgroups

   • Antoine Derighetti

   Pages 101-144

9. CV _p (G) as a Subspace of CV2(G)

   • Antoine Derighetti

   Pages 145-160

10. Back Matter

    Pages 161-171

    PDF

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

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)

• EPFL SB-DO, MA A1 354 (Bâtiment MA) Station 8, Ecole polytechnique fédérale de Lausanne, Lausanne, Switzerland

  Antoine Derighetti

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