On the basis of Hua Loo-Keng's results on harmonic analysis on classical groups, the author Gong Sheng develops his subject further, drawing together results of his own research as well as works from other Chinese mathematicians. The book is divided into three parts studying harmonic analysis of various groups. Starting with the discussion on unitary groups in part 1, the author moves on to rotation groups and unitary symplectic groups in parts 2 and 3, providing a survey of harmonic analysis on characteristic manifold of classical domain of first type for real fields, complex fields and...

This interesting book deals with the theory of convex and starlike biholomorphic mappings in several complex variables. The underly ing theme is the extension to several complex variables of geometric aspects of the classical theory of univalent functions. Because the author's introduction provides an excellent overview of the content of the book, I will not duplicate the effort here. Rather, I will place the book into historical context. The theory of univalent functions long has been an important part of the study of holomorphic functions of one complex variable. The roots of the subject go...