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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

Integral Operator Representation Theorem Translation Operator Multidimensional Case Lebesgue Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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