Fourier Analysis on Finite Abelian Groups (Applied and Numerical Harmonic Analysis) - Hardcover

From the reviews:

"The book under review covers, qua orientation, a pretty broad spectrum ... . The author, Bao Luong, targets well-prepared upper-division students and certain ‘outsiders’ (scientists and engineers) and has taken pains to make his presentation accessible. ... this compact book is indeed very readable ... . there are fifty-six exercises scattered throughout the text, generally quite sporty." (Michael Berg, The Mathematical Association of America, October, 2009)

“The presentation is entirely theoretical ... . What the book does do is cover the Fourier transform (FT) on finite abelian groups, with some emphasis on Gaussian quadratic sums (eigenvalues of the FT) and eigenspaces of the FT operator. There are 56 exercises of varying difficulty spread throughout the book. ... may be helpful for that student’s review at the end of the course and for the instructor, mathematicians, and many scientists and engineers.” (Colin C. Graham, Mathematical Reviews, Issue 2011 e)

This unified, self-contained book examines the mathematical tools used for decomposing and analyzing functions, specifically, the application of the [discrete] Fourier transform to finite Abelian groups. With countless examples and unique exercise sets at the end of each section, Fourier Analysis on Finite Abelian Groups is a perfect companion to a first course in Fourier analysis. This text introduces mathematics students to subjects that are within their reach, but it also has powerful applications that may appeal to advanced researchers and mathematicians. The only prerequisites necessary are group theory, linear algebra, and complex analysis.