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In this chapter we introduce the notion of the Mellin differential operator. It is based on the notion of Mellin translation which represents the Mellin counterpart of the classical translation operator \(\mathcal {T}_h\) defined by \(\mathcal {T}_hf(x) = f(x+h).\) We begin a section about the basic theory of the spaces on which Mellin analysis is built.

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The Foundation of Mellin Analysis

  • 章节

  • 发表日期：

    2025年

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  • Carlo Bardaro,
  • Paul L. Butzer,
  • Ilaria Mantellini,
  • Gerhard Schmeisser

摘要

In this chapter we introduce the notion of the Mellin differential operator. It is based on the notion of Mellin translation which represents the Mellin counterpart of the classical translation operator \(\mathcal {T}_h\) defined by \(\mathcal {T}_hf(x) = f(x+h).\) We begin a section about the basic theory of the spaces on which Mellin analysis is built.