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<p>The pioneer work of János Aczél on functional equations led to a comprehensive theory on this field. His basic book “Lectures on functional equations and their applications” served as a cornerstone of this theory. A great number of classical functional equations are of or can be reduced to convolution-type systems of functional equations. It turned out that this class can effectively be studied using the methods of harmonic analysis and spectral synthesis. In this paper we give a short summary starting from the basics of the theory to the present state and main results.</p>

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Convolution-type functional equations

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年8月25日

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  • László Székelyhidi

摘要

The pioneer work of János Aczél on functional equations led to a comprehensive theory on this field. His basic book “Lectures on functional equations and their applications” served as a cornerstone of this theory. A great number of classical functional equations are of or can be reduced to convolution-type systems of functional equations. It turned out that this class can effectively be studied using the methods of harmonic analysis and spectral synthesis. In this paper we give a short summary starting from the basics of the theory to the present state and main results.