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In this chapter, we first introduce the finite Mellin transform of functions in \( Y_c\) and present its basic properties. Then we consider an inversion of this transform which leads us to Mellin–Fourier series. After establishing approximations by partial sums represented by finite Mellin convolutions with appropriate kernels, we study convergence of Mellin–Fourier series in the spaces \(Y_c\) and \(Y_c^2\) .

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The Finite Mellin Transform and the Mellin–Fourier Series

  • 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 first introduce the finite Mellin transform of functions in \( Y_c\) and present its basic properties. Then we consider an inversion of this transform which leads us to Mellin–Fourier series. After establishing approximations by partial sums represented by finite Mellin convolutions with appropriate kernels, we study convergence of Mellin–Fourier series in the spaces \(Y_c\) and \(Y_c^2\) .