Classical and Approximate Exponential Sampling Formula: Their Interconnections in Uniform and Mellin–Lebesgue Norms

Bardaro C, Butzer PL, Mantellini I, Schmeißer G, Stens RL (2023)


Publication Type: Book chapter / Article in edited volumes

Publication year: 2023

Publisher: Birkhauser

Series: Applied and Numerical Harmonic Analysis

Book Volume: Part F2077

Pages Range: 3-22

DOI: 10.1007/978-3-031-41130-4_1

Abstract

We show that the exponential sampling theorem and its approximate version for functions belonging to a Mellin inversion class are equivalent in the sense that, within the setting of Mellin analysis, each can be obtained from the other as a corollary. The approximate version is considered for both, convergence in the uniform norm and in the Mellin–Lebesgue norm. An important tool is the introduction of a Mellin version of the mixed Hilbert transform and its continuity properties. Our chapter extends the analogous equivalence between the classical and the approximate sampling theorem of Fourier analysis.

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APA:

Bardaro, C., Butzer, P.L., Mantellini, I., Schmeißer, G., & Stens, R.L. (2023). Classical and Approximate Exponential Sampling Formula: Their Interconnections in Uniform and Mellin–Lebesgue Norms. In (pp. 3-22). Birkhauser.

MLA:

Bardaro, C., et al. "Classical and Approximate Exponential Sampling Formula: Their Interconnections in Uniform and Mellin–Lebesgue Norms." Birkhauser, 2023. 3-22.

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