**Translations of Mathematical Monographs**

1998;
256 pp;
Softcover

MSC: Primary 26; 28;
Secondary 42; 46

**Print ISBN: 978-0-8218-2104-6
Product Code: MMONO/177.S**

List Price: $95.00

Individual Member Price: $76.00

# Real Analysis—With an Introduction to Wavelet Theory

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*Satoru Igari*

This introduction to real analysis is based on a series of lectures by the author at Tohoku University. The text covers real numbers, the notion of general topology, and a brief treatment of the Riemann integral, followed by chapters on the classical theory of the Lebesgue integral on Euclidean spaces; the differentiation theorem and functions of bounded variation; Lebesgue spaces; distribution theory; the classical theory of the Fourier transform and Fourier series; and wavelet theory.

The core subjects of real analysis.

The fundamentals for students who are interested in harmonic analysis, probability or partial differential equations.

This volume would be a suitable textbook for an advanced undergraduate or first year graduate course in analysis.

#### Table of Contents

# Table of Contents

## Real Analysis -- With an Introduction to Wavelet Theory

#### Readership

Advanced undergraduates and graduate students studying real analysis; physicists, engineers.

#### Reviews

The presentation is clear and rigorous.

-- SIAM Review

The author has done a fine job in presenting the material selected for this book. The reader is exposed to a variety of real analysis concepts, methods, and techniques. The value of Igari's book lies in this exposition; it combines, contrasts, and reveals those concepts that are vital for a future deeper study of real analysis and its applications. The presentation of the material is clear and precise; well-chosen examples and exercises help the student to master the subject matter at hand … highly recommend this textbook to anyone who is interested in learning about the fundamentals of real and functional analysis, distribution and Fourier theory, and their applications to wavelet theory.

-- Mathematical Reviews

The book is a nice and compact introduction to Real Analysis. The material has been selected with a good taste and presented in a clear form. Each chapter is supplied with a list of problems, the solutions to which are presented at the end of the book. The bibliography reflects recent developments and contains the titles of the best books in the area.

-- Zentralblatt MATH