On asymptotic properties of interpolation polynomials
This paper contains a substantial result caracterizing the interpolation polynomials of holomorphic functions of complex variable: the strong asymptotics formula which generalizes Kakehashi weak asymptotics formula. It is shown also that the Kakehashi condition relevant to the table of interpolation nodes assuming the locally uniforme convergence of certain particular rational function play the key role in the proofs of the above asymptotics. A limit distribution of the interpolation polynomials obtained as corrolary of the main theorem generalizes the classical Jentsch-Szegö theorem on the distribution of zeros of partial sums of Taylor series. The author presents also the proof of Gonchar's unpublished result concerning the generalization of the Cauchy-Hadamard formula for calculating the so called ``radius of the maximal canonical domain'' to the case of an arbitrary continuum if the Kakehashi condition is satisfied.
scientific article; zbMATH DE number 5352324
scientific article