Abstract
In this paper we perform a comparative analysis of Lebesgue functions and constants of a family of Lagrange polynomials. We prove that if a polynomial from the family has the minimal norm in the space of square summable functions, then it also has the minimal norm as an operator which maps the space of continuous functions into itself.
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References
A. Zygmund, Trigonometric Series (Cambridge University Press, Cambridge, 1959; Mir, Moscow, 1965), Vol. 2.
I. A. Shakirov, “Quadrature Formulas for a Singular Integral with Shift, and Applications,” Differents. Uravneniya 27(4), 682–691 (1991).
V. K. Dzyadyk, Approximative Solution Methods for Differential and Integral Equations (Nauk. Dumka, Kiev, 1988) [in Russian].
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Original Russian Text © I.A. Shakirov, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 10, pp. 60–68.
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Shakirov, I.A. The Lagrange trigonometric interpolation polynomial with the minimal norm considered as an operator from C 2π to C 2π . Russ Math. 54, 52–59 (2010). https://doi.org/10.3103/S1066369X10100063
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DOI: https://doi.org/10.3103/S1066369X10100063