Boundedness of Lebesgue constants and interpolating Faber bases
  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. 
Viktoriia Bilet, Oleksiy Dovgoshey, J\"urgen Prestin
math.CA