2.11. Necessary conditions for interpolation by entire functions

Necessary and Sufficient Conditions for Carlson's Theorem on Entire Functions.

A star on a Y (or a IT) wl'' be used throughout this paper to indicate that the index of the sum (or the product) is restricted to lie in A. Theorem 1 is an optimal extension of a celebrated theorem of Carlson which states that the only entire function/(z) satisfying (1.1) and (1.2) and such that/(ra) =0 for each positive integer ra is the null function f(z) =0. The necessity of condition (1.4)...

Interpolation and Approximation by Entire Functions

In this note we study the connection between best approximation and interpolation by entire functions on the real line. A general representation for entire interpolants is outlined. As an illustration, best upper and lower approximations from the class of functions of fixed exponential type to the Gaussian are constructed. §1. Approximation Background The Fourier transform of φ ∈ L(R) is define...

Interpolation of entire functions, product formula for basic sine function

INTERPOLATION BY HYPERBOLIC B-SPLINE FUNCTIONS

In this paper we present a new kind of B-splines, called hyperbolic B-splines generated over the space spanned by hyperbolic functions and we use it to interpolate an arbitrary function on a set of points. Numerical tests for illustrating hyperbolic B-spline are presented.

q-Taylor theorems, polynomial expansions, and interpolation of entire functions

We establish q-analogues of Taylor series expansions in special polynomial bases for functions analytic in bounded domains and for entire functions whose maximum modulus Mðr; f Þ satisfies jln Mðr; f ÞjpA ln r: This solves the problem of constructing such entire functions from their values at 1⁄2aq þ q =a =2; for 0oqo1: Our technique is constructive and gives an explicit representation of the s...