Fourier Analysis: Volume 1, Theory

Adrian Constantin

2016년 5월 · London Mathematical Society Student Texts 85권 · Cambridge University Press

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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.

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Adrian Constantin is currently Professor of Mathematics at the University of Vienna. He is an ISI Highly Cited Researcher and was invited to be plenary speaker at the 6th European Congress of Mathematics. He has received a number of international awards, including the Fluid Dynamics Research prize of the Japanese Society of Fluid Mechanics, the F. W. Bessel Research Award of the Humboldt Foundation (Germany), and the G. Gustafsson Prize of the Royal Swedish Academy of Sciences.