Discrete harmonic analysis: representations, number theory, expanders, and the fourier transform
Series: Cambridge studies in advanced mathematics ; 172Publication details: Cambridge University Press, 2018. Cambridge:Description: xiii, 573p. : ill. ; hb, 23 cmISBN:- 9781107182332
- 515.2433 CEC
Item type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode |
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Books | IIT Gandhinagar General Stacks | General | 515.2433 CEC (Browse shelf(Opens below)) | 1 | Available | 030087 |
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515.2433 JEN Ripples in mathematics: the discrete wavelet transform | 515.2433 BLE Analysis in integer and fractional dimensions | 515.2433 BOC Harmonic analysis and the theory of probability | 515.2433 CEC Discrete harmonic analysis: representations, number theory, expanders, and the fourier transform | 515.2433 DEM Fourier restriction, decoupling, and applications | 515.2433 DUI Fourier integral operators | 515.2433 IOR Fourier analysis and partial differential equations |
Includes bibliographical references and index.
This self-contained book introduces readers to discrete harmonic analysis with an emphasis on the Discrete Fourier Transform and the Fast Fourier Transform on finite groups and finite fields, as well as their noncommutative versions. It also features applications to number theory, graph theory, and representation theory of finite groups. Beginning with elementary material on algebra and number theory, the book then delves into advanced topics from the frontiers of current research, including spectral analysis of the DFT, spectral graph theory and expanders, representation theory of finite groups and multiplicity-free triples, Tao's uncertainty principle for cyclic groups, harmonic analysis on GL(2,Fq), and applications of the Heisenberg group to DFT and FFT. With numerous examples, figures, and over 160 exercises to aid understanding, this book will be a valuable reference for graduate students and researchers in mathematics, engineering, and computer science.
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