Pointwise convergence of derivatives of Lagrange interpolation polynomials for exponential weights

Abstract

For a general class of exponential weights on the line and on (-1, 1), we study pointwise convergence of the derivatives of Lagrange interpolation. Our weights include even weights of smooth polynomial decay near +/-infinity (Freud weights), even weights of faster than smooth polynomial decay near +/-infinity (Erdos weights) and even weights which vanish strongly near 1, for example Pollaczek type weights.