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Discrete Harmonic Analysis: Representations, Number Theory, Expanders, and the Fourier Transform (Cambridge Studies in Advanced Mathematics)
Get Free Ebook Discrete Harmonic Analysis: Representations, Number Theory, Expanders, and the Fourier Transform (Cambridge Studies in Advanced Mathematics)
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Review
'Although the roots of harmonic analysis lie in the continuous world, in the last few decades the field has also started to play a fundamental role in the discrete one. This book gives a panoramic view of Discrete Harmonic Analysis - an area that touches many branches of mathematics, such as number theory, spectral theory, groups and their representations, and graphs. The authors open a door for the reader taking him or her on a beautiful tour of classical and modern mathematics All this is done in a self-contained way that prepares the reader for cutting-edge research.' Alex Lubotzky, Hebrew University of Jerusalem'This book collects a number of gems in number theory and discrete mathematics that have never been put under the same roof, as far as I know. A distinct feature is that it puts harmonic analysis in the foreground where most textbooks present it as ancillary results. The authors must be complimented for their taste in the selection of topics.' Alain Valette, Université de Neuchâtel, Switzerland'This impressive book unites the qualities of a textbook and a research monograph into one comprehensive text. The central theme is the character theory of finite groups and fields, along with various applications. It offers careful and self-contained introductions to all required basics, which can serve for a series of courses. At the same time, it conducts the reader through several modern research themes and results, ranging from Tao's uncertainty principle via expander graphs to Hecke algebras and a detailed study of the representation theory of linear groups over finite fields.' Wolfgang Woess, Technische Universität Graz'The book is split up into four parts ... 'Finite abelian groups and the DFT', 'Finite fields and their characters', 'Graphs and expanders', and 'Harmonic analysis on finite linear groups'. So it's clear that the book covers a lot of ground, and should indeed be of great interest to number theorists, fledgling and otherwise. ... While the book is written 'to be as self-contained as possible' , requiring just linear algebra up to and including the spectral theorem, basic group and ring theory, and 'elementary number theory', the reader is exposed to a lot of serious mathematics, some even at or near the frontier.' Michael Berg, MAA Reviews
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Book Description
This self-contained book introduces discrete harmonic analysis with an emphasis on the Discrete Fourier Transform and the Fast Fourier Transform. Featuring plenty of examples and over 160 exercises, this book will be a valuable reference for graduate students and researchers in mathematics, engineering, and computer science.
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Product details
Series: Cambridge Studies in Advanced Mathematics (Book 172)
Hardcover: 586 pages
Publisher: Cambridge University Press; 1 edition (June 21, 2018)
Language: English
ISBN-10: 1107182336
ISBN-13: 978-1107182332
Product Dimensions:
6.1 x 1.4 x 9.2 inches
Shipping Weight: 2.1 pounds (View shipping rates and policies)
Average Customer Review:
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Amazon Best Sellers Rank:
#1,379,614 in Books (See Top 100 in Books)
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