Boundedness of Lebesgue Constants and Interpolating Faber Bases

Viktoriia V. Bilet, Oleksiy A. Dovgoshey, Jürgen Prestin

Abstract


Background. We investigate the relationship between the boundedness of Lebesgue constants for the Lagrange polynomial interpolation on a compact subset of

\[\mathbb R\]

and the existence of a Faber basis in the space of continuous functions on this compact set.

Objective. The aim of the paper is to describe the conditions on the matrix of interpolation nodes under which the interpolation of any continuous function coincides with the decomposition of this function in a series on the Faber basis.

Methods. The methods of general theory of Schauder bases and the results which describe the convergence of interpolating Lagrange processes are used.

Results. The structure of matrices of interpolation nodes which generate the interpolating Faber bases is described.

Conclusions. Every interpolating Faber basis is generated by the interpolating Lagrange process with the interpolating matrix of a special kind and bounded Lebesgue constants.


Keywords


Lebesgue constant; Lebesgue function; Lagrange polynomial interpolation; Faber basis

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DOI: https://doi.org/10.20535/1810-0546.2017.4.108444

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