  Unlike the classical polynomial case there has not been invented up to very
recently a tool similar to the Bernstein-Bezier representation which would
allow us to control the behavior of the exponential polynomials. The
exponential analog to the classical Bernstein polynomials has been introduced
in a recent authors' paper which appeared in Constructive Approximations, and
this analog retains all basic properties of the classical Bernstein
polynomials. The main purpose of the present paper is to contribute in this
direction, by proving some important properties of the "Bernstein exponential
operator" which has been introduced. We also fix our attention upon some
special type of exponential polynomials which are particularly important for
the further development of theory of representation of Multivariate data.
