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Metric Spaces
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Metric Spaces
Encouraged by the response to the first edition the authors have thoroughly revised Metric Spaces by incorporating suggestions received from the readers.
Functional Analysis
The Book Is Intended To Serve As A Textbook For An Introductory Course In Functional Analysis For The Senior Undergraduate And Graduate Students. It Can Also Be Useful For The Senior Students Of Applied Mathematics, Statistics, Operations Research, Engineering And Theoretical Physics. The Text Starts With A Chapter On Preliminaries Discussing Basic Concepts And Results Which Would Be Taken For Granted Later In The Book. This Is Followed By Chapters On Normed And Banach Spaces, Bounded Linear Operators, Bounded Linear Functionals. The Concept And Specific Geometry Of Hilbert Spaces, Functionals And Operators On Hilbert Spaces And Introduction To Spectral Theory. An Appendix Has Been Given On Schauder Bases.The Salient Features Of The Book Are: * Presentation Of The Subject In A Natural Way * Description Of The Concepts With Justification * Clear And Precise Exposition Avoiding Pendantry * Various Examples And Counter Examples * Graded Problems Throughout Each ChapterNotes And Remarks Within The Text Enhances The Utility Of The Book For The Students.
Theory of Bases in Banach Spaces
The aim of this book is three fold:To serve as a textbook for a course on ?Bases in Banach Spaces? at MA/MSc and MPhil levels.To help the beginners and to those who just want to have a quick idea about bases and use them in other areas.To present the development regarding the most important among the several problems which gained importance, following the negative solution of the basis problem, in the eighties and afterwards. The entire book has been divided into three parts Part I contains Basics in Functional Analysis, which is presented very briefly, so as to make it self-contained Parts II and III contain the topics mentioned in the above objectives of the book. There are seventeen chapters altogether in the book.
Lebesgue Measure and Integration
Key Features:Lebesgue Measure and Integration theory explained for beginners.The text is arranged in sections with a chapter on preliminaries.Numerous examples and problems for effective learning..Bibliography at the end gives contributions of authors to the subject.About the Book:The book is intended to provide a basic course in Lebesgue Measure and Integration for the Honours and Postgraduate students of various universities in India and abroad with the hope that it will open a path to the Lebesgue Theory to the students. Pains have been taken to give detailed explanations of reasons of work and of the method used together with numerous examples and counter examples at different places in ...
General Measure and Integration
he book is intended to serve as a textbook for a course on Measure and Integration, for the graduate and M Phil level students at various Universities. It can be equally useful as a reference book for those who are involved in research in areas requiring the Lebesgue Theory of Integration in its generality. Pains have been taken to give detailed explanations of reasons of work and of the method used. Details are explicitly presented keeping the interest of students in view. The material has been arranged by sections, spread out in eleven chapters. The text starts with a chapter on preliminaries discussing basic concepts and results which would be taken for granted later. This is followed by chapters on Lebesgue Measurable Sets, Measure Spaces, Measurable Functions, Integration, Signed Measures, The Spaces Lp , Product Measure Spaces and Lebesgue-Stieltjes Integral.
Analysis and Applications
Analysis and its applications have been major areas for research in mathematics and allied fields. The fast growing power of computation has made a significant and useful impact in these areas. This has lead to computational analysis and the emergence of fields like Bezier-Bernstein methods for computer-aided geometric design, constructive approximation and wavelets, and even computational harmonic analysis. Analysis and Applications consists of research articles, including a few survey articles, by eminent mathematicians projecting trends in constructive and computational approximation, summability theory, optimal control and theory and applications of function spaces and wavelets.
Analysis and Applications
Papers presented in a conference organized at Ujjain, India, in 1999, to honor Tribikram Pati, b. 1929, Indian mathematician, on his seventieth birth day.
