Representation Theorems

Roald M. Trigub and Eduard S. Bellinsky
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Roald M. Trigub: Donetsk National University
Eduard S. Bellinsky: University of West Indies

Chapter Chapter 1 in Fourier Analysis and Approximation of Functions, 2004, pp 1-24 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-1-4020-2876-2_1

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