文章基本信息
- 标题：The Riesz Representation Operator on the Dual of C[0; 1] is Computable
- 本地全文：下载
- 作者：Tahereh Jafarikhah ; Klaus Weihrauch
- 期刊名称：Journal of Universal Computer Science
- 印刷版ISSN：0948-6968
- 出版年度：2013
- 卷号：19
- 期号：6
- 页码：750-770
- 出版社：Graz University of Technology and Know-Center
- 摘要：By the Riesz representation theorem, for every linear functional F : C[0; 1] → ℝ there is a function g : [0; 1] → ℝ of bounded variation such that
A computable version is proved in [Lu and Weihrauch(2007)]: a function g can be computed from F and its norm, and F can be computed from g and an upper bound of its total variation. In this article we present a much more transparent proof. We first give a new proof of the classical theorem from which we then can derive the computable version easily. As in [Lu and Weihrauch(2007)] we use the framework of TTE, the representation approach for computable analysis, which allows to define natural concepts of computability for the operators under consideration.
