Interpolation by Generalized Splines.
In the paper we present a derivative-free estimate of the remainder of an arbitrary interpolation rule on the class of entire functions which, moreover, belong to the space . The theory is based on the use of the Paley-Wiener theorem. The essential advantage of this method is the fact that the estimate of the remainder is formed by a product of two terms. The first term depends on the rule only while the second depends on the interpolated function only. The obtained estimate of the remainder of...
This paper deals with an interpolation problem in the open unit disc of the complex plane. We characterize the sequences in a Stolz angle of , verifying that the bounded sequences are interpolated on them by a certain class of not bounded holomorphic functions on , but very close to the bounded ones. We prove that these interpolating sequences are also uniformly separated, as in the case of the interpolation by bounded holomorphic functions.
We give a pure complex variable proof of a theorem by Ismail and Stanton and apply this result in the field of integer-valued entire functions. Our proof rests on a very general interpolation result for entire functions.