Harmonic analysis on compact solvmanifolds / Jonathan Brezin

This book is a survey of inductive methods in harmonic analysis on compact homogeneous spaces, especially methods applicable to compact solvmanifolds. The first part of the book, comprising more than half of the total, is devoted to several three- and four- dimensional examples of solvmanifolds. This reflects the author's conviction about the importance of these examples and the phenomena illustrated therein, and it results in a book which should be singularly useful as an introduction to the field. The second part of the book treats general inductive methods for compact homogeneous spaces (quotients of locally compact groups), and the third part applies these methods to general compact nilmanifolds and solvmanifolds. The book concludes with a brief historical survey and a bibliography. There are some prerequisites from Lie theory, representation theory, and number theory, but none too deep to be picked up as one goes along. ... (MathSciNet)