Constructive Approximation
Constructive Approximation
复制标题
DOI：
10.1007/978-3-662-02888-9
复制
发表时间：
1993
期刊：
影响因子：
39.8
通讯作者：
R. DeVore;G. Lorentz
中科院分区：
文献类型：
--
作者：
R. DeVore;G. Lorentz
本书涉及一些基本问题的逼近理论：与性质的多项式和样条，与逼近的poly-mials，样条，线性算子。同时也为不同功能空间的设计提供了必要的素材.从某种意义上说，这是我们中的一个人（洛伦兹[A-1966]）的书的相应部分的现代版本。我们已经试图给出一个完整的阐述的主要，基本定理的理论，没有进入太多的细节，治疗最一般的情况下，或讨论非常特殊的问题。有本质的限制：这是一本关于一个真实的变量的函数近似的书。但逼近理论的职能，几个真实的或复杂的变量将需要新的书籍。关于插值的内容很少。但即使有了这些限制，一些深刻而重要的结果，如Korneichuk关于Lipschitz空间中逼近的定理的证明，也不能包括在内。另一本书，与不同的作者，“建设性近似，先进的问题”，是在筹备中。有一个广泛的参考书目，这也可以用作作者索引：每篇论文都提供了参考的页面或页面，它已经被使用。
The present book deals with some basic problems of Approximation Theory: with properties of polynomials and splines, with approximation by poly-mials, splines, linear operators. It also provides the necessary material ab out different function spaces. In some sense, this is a modern version of the corre sponding parts of the book of one of us (Lorentz [A-1966]). We have tried to give a complete exposition of the main, basic theorems of the theory, without going into too much detail, treating the most general cases or discussing very special problems. There are essential limitations: this is a book about approximation of functions of one real variable. But Approxima tion Theory of functions of several real or of complex variables would require new books. Very little is given on interpolation. But even with these restric tions, proofs of some deep and important results, like Korneichuk's theorems about approximation in Lipschitz spaces, could not be included. Another book, with different authors," Constructive Approximation, Advanced Problems", is in preparation. There is an extensive bibliography, which can be used also as an Author Index: each paper is supplied with references for the page or pages where it has been used.