Approximation with Positive Linear Operators and Linear Combinations
暫譯: 正線性算子與線性組合的近似法則

Gupta, Vijay, Tachev, Gancho

  • 出版商: Springer
  • 出版日期: 2018-08-02
  • 售價: $4,600
  • 貴賓價: 9.5$4,370
  • 語言: 英文
  • 頁數: 186
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3319864769
  • ISBN-13: 9783319864761
  • 海外代購書籍(需單獨結帳)

商品描述

This book presents a systematic overview of approximation by linear combinations of positive linear operators, a useful tool used to increase the order of approximation. Fundamental and recent results from the past decade are described with their corresponding proofs. The volume consists of eight chapters that provide detailed insight into the representation of monomials of the operators Ln, direct and inverse estimates for a broad class of positive linear operators, and case studies involving finite and unbounded intervals of real and complex functions. Strong converse inequalities of Type A in terminology of Ditzian-Ivanov for linear combinations of Bernstein and Bernstein-Kantorovich operators and various Voronovskaja-type estimates for some linear combinations are analyzed and explained. Graduate students and researchers in approximation theory will find the list of open problems in approximation of linear combinations useful. The book serves as a reference for graduate and postgraduate courses as well as a basis for future study and development.

商品描述(中文翻譯)

本書系統性地概述了透過正線性算子的線性組合進行近似的方法,這是一種用於提高近似階數的有用工具。書中描述了過去十年來的基本和最新結果,並附上相應的證明。本書共分為八章,詳細介紹了算子 Ln 的單項式表示、廣泛類別的正線性算子的直接和反向估計,以及涉及實數和複數函數的有限和無界區間的案例研究。分析並解釋了 Ditzian-Ivanov 術語中類型 A 的強對偶不等式,這些不等式涉及 Bernstein 和 Bernstein-Kantorovich 算子的線性組合,以及一些線性組合的各種 Voronovskaja 類型估計。研究生和近似理論的研究人員將會發現,書中列出的線性組合近似的開放問題清單非常有用。本書可作為研究生和研究所課程的參考資料,也可作為未來研究和發展的基礎。