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In the development of Mellin analysis, in particular in studies in the spirit of the Paley–Wiener theorem, we shall come across the problem of characterizing functions that are originally defined on \(\mathbb {R}^+\) but can be extended to a larger domain in an analytic way. For this, the classical notion of analyticity will turn out to be quite awkward. A modified concept, which we shall describe in this chapter, leads to more elegant and concise results.

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Polar-Analytic Functions

  • 章节

  • 发表日期：

    2025年

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

摘要

In the development of Mellin analysis, in particular in studies in the spirit of the Paley–Wiener theorem, we shall come across the problem of characterizing functions that are originally defined on \(\mathbb {R}^+\) but can be extended to a larger domain in an analytic way. For this, the classical notion of analyticity will turn out to be quite awkward. A modified concept, which we shall describe in this chapter, leads to more elegant and concise results.