Function theory of several complex variables. 2. ed. (English) Zbl 0776.32001

Krantz, Steven G.

Wadsworth & Brooks/Cole Mathematics Series. Pacific Grove, CA: Wadsworth & Brooks/Cole Advanced Books & Software. xv, 557 p. (1992).

This is a welcome new edition of the author’s popular graduate textbook on the function theoretic aspects of several complex variables [first edition, Wiley (1982; Zbl 0471.32008)]. Besides updating the text and making minor emendations, the author has added some material. There is a new chapter about the inner function problem and the constructive methods that where used to solve it. Also, the concluding chapter has new sections that briefly treat complex analytic dynamics in two complex variables, the notion of finite type, and the work of Lempert on the Kobayashi metric.

Reviewer: H.P.Boas (College Station)

MSC:

32-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to several complex variables and analytic spaces
37F99	Dynamical systems over complex numbers
32F45	Invariant metrics and pseudodistances in several complex variables

Keywords:

holomorphic functions; textbook; inner function; complex analytic dynamics; finite type; Kobayashi metric

Citations:

Zbl 0471.32008