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Fourier analysis aims to decompose functions into a superposition of simple trigonometric functions, whose special features can be exploited to isolate specific components into manageable clusters before reassembling the pieces. This two-volume text presents a largely self-contained treatment, comprising not just the major theoretical aspects (Part I) but also exploring links to other areas of mathematics and applications to science and technology (Part II). Following the historical and conceptual genesis, this book (Part I) provides overviews of basic measure theory and functional analysis, with added insight into complex analysis and the theory of distributions. The material is intended for both beginning and advanced graduate students with a thorough knowledge of advanced calculus and linear algebra. Historical notes are provided and topics are illustrated at every stage by examples and exercises, with separate hints and solutions, thus making the exposition useful both as a course textbook and for individual study.
.Achieves a balance between pure and applied topics, appealing to mathematicians working in all areas
.Includes a large number of exercises, with separate hints and solutions, to improve understanding
.Provides an overview of topics intertwined with Fourier analysis, such as measure theory, functional analysis and complex analysis
1. Introduction
2. The Lebesgue measure and integral
3. Elements of functional analysis
4. Convergence results for Fourier series
5. Fourier transforms
6. Multi-dimensional Fourier analysis
7. A glance at some advanced topics
Appendix: historical notes
References
Index.
Description
Fourier analysis aims to decompose functions into a superposition of simple trigonometric functions, whose special features can be exploited to isolate specific components into manageable clusters before reassembling the pieces. This two-volume text presents a largely self-contained treatment, comprising not just the major theoretical aspects (Part I) but also exploring links to other areas of mathematics and applications to science and technology (Part II). Following the historical and conceptual genesis, this book (Part I) provides overviews of basic measure theory and functional analysis, with added insight into complex analysis and the theory of distributions. The material is intended for both beginning and advanced graduate students with a thorough knowledge of advanced calculus and linear algebra. Historical notes are provided and topics are illustrated at every stage by examples and exercises, with separate hints and solutions, thus making the exposition useful both as a course textbook and for individual study.
.Achieves a balance between pure and applied topics, appealing to mathematicians working in all areas
.Includes a large number of exercises, with separate hints and solutions, to improve understanding
.Provides an overview of topics intertwined with Fourier analysis, such as measure theory, functional analysis and complex analysis
