AMS Chelsea Publishing 1962; 496 pp; hardcover Volume: 270 Reprint/Revision History: Reprinted 2005 ISBN10: 0821829149 ISBN13: 9780821829141 List Price: US$69 Member Price: US$62.10 Order Code: CHEL/270.H
 This famous work is a textbook that emphasizes the conceptual and historical continuity of analytic function theory. The second volume broadens from a textbook to a textbooktreatise, covering the "canonical" topics (including elliptic functions, entire and meromorphic functions, as well as conformal mapping, etc.) and other topics nearer the expanding frontier of analytic function theory. In the latter category are the chapters on majorization and on functions holomorphic in a halfplane. Table of Contents Volume II  10. Analytic continuation: 10.1 Introduction; 10.2 Rearrangements of power series; 10.3 Analytic functions; 10.4 Singularities; 10.5 Borel monogenic functions; 10.6 Multivalued functions and Riemann surfaces; 10.7 Law of permanence of functional equations
 11. Singularities and representation of analytic functions: 11.1 Holomorphypreserving transformations: I. Integral operators; 11.2 Holomorphypreserving transformations: II. Differential operators; 11.3 Power series with analytic coefficients; 11.4 Analytic continuation in a star; 11.5 Polynomial series; 11.6 Composition theorems; 11.7 Gap theorems and noncontinuable power series
 12. Algebraic functions: 12.1 Local properties; 12.2 Critical points; 12.3 Newton's diagram; 12.4 Riemann surfaces; some concepts of algebraic geometry; 12.5 Rational functions on the surface and Abelian integrals
 13. Elliptic functions: 13.1 Doublyperiodic functions; 13.2 The functions of Weierstrass; 13.3 Some further properties of elliptic functions; 13.4 On the functions of Jacobi; 13.5 The theta functions; 13.6 Modular functions
 14. Entire and meromorphic functions: 14.1 Order relations for entire functions; 14.2 Entire functions of finite order; 14.3 Functions with real zeros; 14.4 Characteristic functions; 14.5 Picard's and Landau's theorems; 14.6 The second fundamental theorem; 14.7 Defect relations
 15. Normal families: 15.1 Schwarz's lemma and hyperbolic measure; 15.2 Normal families; 15.3 Induced convergence; 15.4 Applications
 16. Lemniscates: 16.1 Chebichev polynomials; 16.2 The transfinite diameter; 16.3 Additive set functions; RadonStieltjes integrals; 16.4 Logarithmic capacity; 16.5 Green's function; Hilbert's theorem; 16.6 Runge's theorem; 16.7 Overconvergence
 17. Conformal mapping: 17.1 Riemann's mapping theorem; 17.2 The kernel function; 17.3 Fekete polynomials and the exterior mapping problem; 17.4 Univalent functions; 17.5 The boundary problem; 17.6 Special mappings; 17.7 The theorem of Bloch
 18. Majorization: 18.1 The PhragménLindelöf principle; 18.2 Dirichlet's problem; Lindelöf's principle; 18.3 Harmonic measure; 18.4 The NevanlinnaAhlforsHeins theorems; 18.5 Subordination
 19. Functions holomorphic in a halfplane: 19.1 The HardyLebesgue classes; 19.2 Bounded functions; 19.3 Growthmeasuring functions; 19.4 Remarks on LaplaceStieltjes integrals
 Bibliography
 Index
