一种控制指数过程的新方法
On a new method for controlling exponential processes
AI总结：
本文提出一种指数型Bernstein算子，用于控制指数多项式的行为，并证明其基本性质，为多元数据表示理论提供基础。
摘要：
与经典多项式情形不同，直到最近才发明了一种类似于Bernstein-Bezier表示的工具，用于控制指数多项式的行为。经典Bernstein多项式的指数类比已在作者近期发表于《Constructive Approximations》的论文中引入，该类比保留了经典Bernstein多项式的所有基本性质。本文的主要目的是通过证明所引入的“Bernstein指数算子”的一些重要性质，为该方向做出贡献。我们还特别关注某些特殊类型的指数多项式，它们对于多元数据表示理论的进一步发展尤为重要。
英文摘要：
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.
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