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Analytic Function Theory, Volume II

Einar Hille
Publisher: 
American Mathematical Society/Chelsea
Publication Date: 
1962
Number of Pages: 
496
Format: 
Hardcover
Price: 
59.00
ISBN: 
0-8218-2914-9
Category: 
Monograph
BLL Rating: 

The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

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  • 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 Holomorphy-preserving transformations: I. Integral operators; 11.2 Holomorphy-preserving 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 Doubly-periodic 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; Radon-Stieltjes 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 Phragmén-Lindelöf principle; 18.2 Dirichlet's problem; Lindelöf's principle; 18.3 Harmonic measure; 18.4 The Nevanlinna-Ahlfors-Heins theorems; 18.5 Subordination
  • 19. Functions holomorphic in a half-plane: 19.1 The Hardy-Lebesgue classes; 19.2 Bounded functions; 19.3 Growth-measuring functions; 19.4 Remarks on Laplace-Stieltjes integrals
  • Bibliography
  • Index

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