Boundedness of Lebesgue constants and interpolating Faber bases

2016/10/17 by Bilet, Viktoriia, Dovgoshey, Oleksiy, Prestin, Jürgen
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1610.05026

Abstract

We investigate some conditions under which the Lebesgue constants or Lebesgue functions are bounded for the classical Lagrange polynomial interpolation on a compact subset of \mathbb R. In particular, relationships of such boundedness with uniform and pointwise convergence of Lagrange polynomials and with the existence of interpolating Faber bases are discussed.

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