Functional Analysis and Summability
暫譯: 函數分析與可總和性
Natarajan, P. N.
- 出版商: CRC
- 出版日期: 2020-09-08
- 售價: $6,190
- 貴賓價: 9.5 折 $5,881
- 語言: 英文
- 頁數: 220
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 0367544490
- ISBN-13: 9780367544492
海外代購書籍(需單獨結帳)
商品描述
There are excellent books on both functional analysis and summability. Most of them are very terse. In Functional Analysis and Summability, the author makes a sincere attempt for a gentle introduction of these topics to the students. In the functional analysis component of the book, the Hahn-Banach theorem, the Banach-Steinhaus theorem (or uniform boundedness principle), the open mapping theorem, the closed graph theorem and the Riesz representation theorem are highlighted. In the summability component of the book, the Silverman-Toeplitz theorem, Schur's theorem, the Steinhaus theorem and Steinhaus type theorems are proved. The utility of functional analytic tools like the uniform boundedness principle to prove some results in summability theory is also pointed out.
Features
- A sincere attempt is made by the author for a soft and gentle introduction of the topics to the student
- Basic results of functional analysis and summability theory are highlighted
- Applications of these results are also brought out
- A lot of examples have been provided in the text wherever needed
- Useful exercises are included at the end of each chapter
The book will be useful to postgraduate students, pre-research level students and research scholars in mathematics. Students of physics and engineering will also find this book useful since topics in the book also have applications in related areas.
商品描述(中文翻譯)
有關函數分析和可加性的優秀書籍很多，其中大多數都非常簡潔。在《Functional Analysis and Summability》一書中，作者誠摯地嘗試為學生提供這些主題的溫和介紹。在書中的函數分析部分，重點介紹了哈恩-巴拿赫定理、巴拿赫-斯坦豪斯定理（或均勻有界性原理）、開映射定理、閉圖像定理以及里茲表示定理。在書中的可加性部分，證明了西爾弗曼-托普利茨定理、舒爾定理、斯坦豪斯定理及斯坦豪斯類型定理。書中還指出了函數分析工具如均勻有界性原理在證明可加性理論某些結果中的實用性。
特點
- 作者誠摯地嘗試為學生提供主題的柔和介紹
- 突出了函數分析和可加性理論的基本結果
- 這些結果的應用也得到了闡述
- 在文本中提供了大量必要的例子
- 每章結尾都包含有用的練習題
本書將對研究生、預研究階段的學生以及數學研究學者有幫助。物理和工程的學生也會發現本書有用，因為書中的主題在相關領域也有應用。
作者簡介
P.N. Natarajan (Pinnangudi Narayanasubramanian Natarajan) is former professor and Head, Department of Mathematics, Ramakrishna Mission Vivekananda College, Chennai. He got Ph.D. in Analysis from the University of Madras in 1980. An active researcher till date, Prof. Natarajan has over 120 research papers to his credit, published in reputed journals like Proceedings of the American Mathematical Society, Journal of the London Mathematical Society, Indagationes Mathematicae, Annales Mathematiques Blaise Pascal, Commentationes Mathematicae (Prace Matematyczne), p-adic Numbers, Ultrametric Analysis and Applications and Journal of the Indian Mathematical Society. He has so far authored 5 books, published by Springer-Verlag, John Wiley and Taylor and Francis. He has also contributed a chapter each to 3 edited volumes, brought out by Springer-Verlag, Birkhauser-Verlag and Taylor and Francis. His research interests include Summability Theory and Functional Analysis, both Classical and Ultrametric. Prof. Natarajan was honoured with the Dr. Radhakrishnan Award for the Best Teacher in Mathematics for the 1990-1991 by the Government of Tamil Nadu. Besides visiting several institutes of repute in Canada, France, Holland and Greece on invitation, Prof. Natarajan has taken part in several International Conferences and has chaired sessions.
作者簡介(中文翻譯)
P.N. Natarajan（Pinnangudi Narayanasubramanian Natarajan）是印度金奈拉馬克里希納使命維韋卡南大學數學系的前教授及系主任。他於1980年在馬德拉斯大學獲得分析學博士學位。至今仍然活躍於研究的Natarajan教授，已發表超過120篇研究論文，這些論文發表在美國數學學會會刊、倫敦數學學會期刊、數學研究、布萊斯·帕斯卡數學年報、數學評論（Prace Matematyczne）、p-adic Numbers、超度量分析及應用以及印度數學學會期刊等知名期刊上。他迄今已著作5本書籍，出版商包括Springer-Verlag、John Wiley和Taylor and Francis。他還為3本編輯書籍各貢獻了一章，這些書籍由Springer-Verlag、Birkhauser-Verlag和Taylor and Francis出版。他的研究興趣包括求和理論和函數分析，涵蓋古典和超度量兩個領域。Natarajan教授曾獲得1990-1991年度泰米爾納德邦政府頒發的最佳數學教師Dr. Radhakrishnan獎。此外，Natarajan教授應邀訪問過加拿大、法國、荷蘭和希臘的多個知名機構，並參加了多個國際會議並擔任會議主席。
