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Optimal Birkhoff Interpolation and Birkhoff Numbers in Some Function Spaces

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Abstract

This paper investigates the optimal Birkhoff interpolation and Birkhoff numbers of some function spaces in space L[−1, 1] and weighted spaces Lp,ω[−1,1], 1 ≤ p < ∞, with ω being a continuous integrable weight function in (−1,1). We proved that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal. We also show that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal when the function values of the two endpoints are included in the interpolation systems.

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Correspondence to Guiqiao Xu.

Additional information

The first author was supported by National Natural Science Foundation of China (11871006, 11671271).

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Xu, G., Liu, Y. & Guo, D. Optimal Birkhoff Interpolation and Birkhoff Numbers in Some Function Spaces. Acta Math Sci 43, 125–142 (2023). https://doi.org/10.1007/s10473-023-0108-5

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  • DOI: https://doi.org/10.1007/s10473-023-0108-5

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