n-Widths in Approximation Theory
n-Widths in Approximation Theory
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DOI：
10.1007/978-3-642-69894-1
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发表时间：
1985-01
期刊：
影响因子：
--
通讯作者：
A. Pinkus
中科院分区：
文献类型：
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作者：
A. Pinkus
我最初对这个主题的介绍是通过保护，并最终与 CA Micchelli 合作。我很感谢他和教授们。 C. de Boor、EW Cheney、SD Fisher 和 AA Melkman 阅读了手稿的各个部分，他们的建议非常有帮助。准确性和遗漏的错误完全由我负责。我谨向英国国家电力研究委员会和兰开斯特大学数学系表示感谢，感谢他们在英国度过了这一年，在此期间完成了本文的大部分手稿，同时也感谢美国陆军欧洲研究办公室对我的研究工作的财政支持。还要感谢玛丽昂·马克斯 (Marion Marks)，她打字了部分手稿。海法，1984 年 Allan Pinkus 目录 1 第一章。简介......第二章。 n 宽度的基本属性。 9 1. d••••••••• 的性质 9 n 15 2. d• nn 最优子空间的存在性 17 3. d•••••• 的性质 20 4. b•••••• n 的性质 5. n 宽度之间的不等式 22 n 6. d 和 d•• 之间的对偶性 27 n 7. d••••• 的 n 宽度单位球的映射 29 8. dn (T)、 dn (T) 和 bn (T)。 32 37 注释和参考文献.........................
My original introduction to this subject was through conservations, and ultimate ly joint work with CA Micchelli. I am grateful to him and to Profs. C. de Boor, EW Cheney, SD Fisher and AA Melkman who read various portions of the manuscript and whose suggestions were most helpful. Errors in accuracy and omissions are totally my responsibility. I would like to express my appreciation to the SERC of Great Britain and to the Department of Mathematics of the University of Lancaster for the year spent there during which large portions of the manuscript were written, and also to the European Research Office of the US Army for its financial support of my research endeavors. Thanks are also due to Marion Marks who typed portions of the manuscript. Haifa, 1984 Allan Pinkus Table of Contents 1 Chapter I. Introduction........ Chapter II. Basic Properties of n-Widths. 9 1. Properties of d•••••••••• 9 n 15 2. Existence of Optimal Subspaces for d• nn 17 3. Properties of d•••••• 20 4. Properties of b•••••• n 5. Inequalities Between n-Widths 22 n 6. Duality Between d and d•• 27 n 7. n-Widths of Mappings of the Unit Ball 29 8. Some Relationships Between dn (T), dn (T) and bn (T). 32 37 Notes and References..............