Infinitely differentiable functions represented into Newton interpolating series

We study infinitely differentiable functions which are representable into a Newton interpolating series at a suitable interpolation sequence with terms in [0, 1]. Applications of this series to approximate the solution of boundary value problems for linear systems of differential equations are presented.

The Nevanlinna-Pick theorem and a non-positive definite matrix

Let {zj} be an interpolation sequence in the open unit disc and {wj} a bounded sequence. In this note, it is shown that there is a function F in H∞ + C satisfying ‖F‖ ≤ 1 and as j → ∞ if and only if there exists a compact matrix [tij] such that on where .

Necessary Conditions for Universal Interpolation in

Let be the space of Fourier transforms of distributions with compact support, or equivalently, the space of entire functions h satisfying the growth condition(1)where p(z) = |Imz| + log (1 + |z|2) and A, B are constants depending only on h. A sequence with |zk| ↑ ∞ is said to be a universal interpolation sequence for if for all such that(2)for constants A, B independent of k, there exists such that f(zk) = ak. In this note we will consider necessary conditions for universal interpolation in and more general subspaces of the entire functions.