抽象凸分析（英文）

定　　价：68 元

丛书名：国外优秀数学著作原版系列 ， “十三五”重点出版物规划项目·他山之石系列

• 作者：[罗] 伊凡·辛格（Ivan Singer） 著
• 出版时间：2020/11/1
• ISBN：9787560391557
• 出 版 社：哈尔滨工业大学出版社

• 中图法分类：O174.13 
• 页码：519
• 纸张：胶版纸
• 版次：1
• 开本：16开

内容简介

　　《抽象凸分析（英文）》主要包括从凸分析到抽象凸分析、一个完整格的元素的抽象凸性、集合子集的抽象凸性、集上函数的抽象凸性、完全晶格之间的对偶性、晶格族之间的对偶、函数集合之间的对偶性、抽象的次微分等内容，也包含了关于当代抽象凸分析非常先进且详尽的考查。
　　《抽象凸分析（英文）》致力于研究通过在一个有序的空间中取得上确界（或下确界）元素族的操作来表示复杂的对象。
　　在《抽象凸分析（英文）》中，读者可以找到对抽象凸性的几种方法的介绍和它们之间的比较。
　　《抽象凸分析（英文）》适合对抽象凸分析感兴趣的数学专业学生及教师参考阅读。

序 言

　　One of the principal methods used in mathematics to represent complex objects involves the application of certain operations to finite or especially infinite sets of simpler objects which can be used to essentially approximate the complex objects. Classical examples of such methods include， among many others， infinite series representations of functions in mathematical analysis and series expansions with respect to a Schauder basis in the study of separable Banach spaces in functional analysis.
　　The author of this monograph is a prominent expert in the study of Schauder bases， but the present book is devoted to a different kind of application of the approach described above， namely to the representation of complex objects through the operation of taking suprema （or infima） of families of elements in an ordered space.
　　In the late 1960s and early 1970s it was realized that it is possible， and relatively straightforward， to obtain many of the principal results of convex duality theory using the representation of a convex function as the point wise supremum of the set of its affine minorants. Moreover， many of these results do not depend on the linear structure of the class of minorizing functions， The corresponding observation for closed convex sets was made even earlier， that is， many results for these sets easily follow from their \"outer\" representation as intersections of closed half-spaces. Also， many of these results can be generalized to sets which can be represented as the intersections of other families of sets that are not necessarily half-spaces.