Representation Theorems

  • Roald M. Trigub
  • Eduard S. Bellinsky

Abstract

One of the central objects of Fourier Analysis is operators of the form
$$ f\left( \right) \mapsto \int\limits_{{R^m}} {f\left( { + \lambda u} \right)d\mu \left( u \right)} $$
(the convolution of a function and a measure) . When λ = 1 these operators commute with the translation operator: \( f\left( \right) \mapsto f\left( { + t} \right)! \) , that is, are translation invariant, and this property characterizes such operators completely.

Keywords

Convolution Stein 

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Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • Roald M. Trigub
    • 1
  • Eduard S. Bellinsky
    • 2
  1. 1.Donetsk National UniversityDonetskUkraine
  2. 2.University of West IndiesBridgetownBarbados

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