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Introduction to Modern Analysis

Shmuel Kantorovitz
Publisher: 
Oxford University Press
Publication Date: 
2006
Number of Pages: 
434
Format: 
Paperback
Series: 
Oxford Graduate Texts in Mathematics 8
Price: 
59.50
ISBN: 
0199203156
Category: 
Textbook
[Reviewed by
Mihaela Poplicher
, on
01/20/2007
]

This book appears in the series Oxford Graduate Texts in Mathematics, and can be used in an advanced undergraduate course or a graduate course in Analysis. It contains the main topics in Analysis arranged in ten chapters, followed by two chapters of "applications" covering Probability and Distributions.

Since it contains so many important topics, is written very well, with complete proofs and explanations, this book is a very valuable contribution to the wide and beautiful field of “modern analysis.” It was developed by the author over many years (since 1964) of teaching analysis courses at several universities.

One more reason to strongly recommend this book: it has solutions to the many exercises at its companion website: http://www.oup.com/uk/booksites/content/0199203156/


Mihaela Poplicher is associate professor of mathematics at the University of Cincinnati. Her research interests include functional analysis, harmonic analysis, and complex analysis. She is also interested in the teaching of mathematics. Her email address is Mihaela.Poplicher@uc.edu.

Preface
1. Measures
2. Construction of measures
3. Measure and topology
4. Continuous linear functionals
5. Duality
6. Bounded operators
7. Banach algebras
8. Hilbert spaces
9. Integral representation
10. Unbounded operators
Application I:Probability
Application II: Distributions
Bibliography
Index

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