Interpolation of Entire Functions and Projective Descriptions

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...

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...

Interpolation of entire functions, product formula for basic sine function

Growth analysis of entire functions of two complex variables

In this paper, we introduce the idea of generalized relative order (respectively generalized relative lower order) of entire functions of two complex variables. Hence, we study some growth properties of entire functions of two complex variables on the basis of the definition of generalized relative order and generalized relative lower order of entire functions of two complex variables.

Quasianalytic Functionals and Projective Descriptions

The topology of the weighted inductive limit of Fréchet spaces of entire functions in N variables which is obtained as the Fourier Laplace transform of the space of quasianalytic functionals on an open convex subset of R cannot be described by means of weighted supseminorms.