Uniform and $$L^p$$ Convergence of the Hermite Interpolation at Pollaczek–Laguerre Zeros

The paper deals with the weighted polynomial approximation of functions defined on (0,+∞), which can grow exponentially both at +∞ and at 0. To this aim, we introduce interpolating operators of Hermite and Hermite–Fejér-type, based at the zeros of Pollaczek–Laguerre type orthogonal polynomials. We prove that these processes converge in weighted uniform and Lp-norms and provide sharp error estimates showing that the order of convergence is the same as the best polynomial approximation, under suitable assumptions.