Discrete Harmonic Analysis by Tullio Ceccherini-Silberstein, ... - 9781107182332

Discrete Harmonic AnalysisRepresentations, Number Theory, Expanders, and the Fourier Transform\nAuthor(s): Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli\nFormat: Hardback\nPublisher: Cambridge University Press, United Kingdom\nImprint: Cambridge University Press\nISBN-13: 9781107182332, 978-1107182332\nSynopsis\nThis 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 c.