Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Analytic Function Theory, Vol II
 
Einar Hille
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Softcover ISBN:  978-0-8218-3344-5
Product Code:  CHEL/270.S
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $62.10
eBook ISBN:  978-1-4704-8014-1
Product Code:  CHEL/270.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Softcover ISBN:  978-0-8218-3344-5
eBook: ISBN:  978-1-4704-8014-1
Product Code:  CHEL/270.S.B
List Price: $134.00 $101.50
MAA Member Price: $120.60 $91.35
AMS Member Price: $120.60 $91.35
Add to cart
Click above image for expanded view
Analytic Function Theory, Vol II
Einar Hille
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Softcover ISBN:  978-0-8218-3344-5
Product Code:  CHEL/270.S
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $62.10
eBook ISBN:  978-1-4704-8014-1
Product Code:  CHEL/270.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Softcover ISBN:  978-0-8218-3344-5
eBook ISBN:  978-1-4704-8014-1
Product Code:  CHEL/270.S.B
List Price: $134.00 $101.50
MAA Member Price: $120.60 $91.35
AMS Member Price: $120.60 $91.35
Add to cart
  • Book Details
     
     
    AMS Chelsea Publishing
    Volume: 270; 1962; 496 pp
    MSC: Primary 30; 01

    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 textbook-treatise, 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 half-plane.
  • Table of Contents
     
     
    • Front Cover
    • Foreword
    • Contents
    • Volume I
    • Volume II
    • Symbols
    • 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.
    • COLLATERAL READING
    • 11 SINGULARITIES AND REPRESENTATION OF ANALYTIC FUNCTIONS
    • 11.1. Holomorphy-preserving transformations: I. Integral operators.
    • 11.2. Holomorphy-preserving transformations: Il. 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 nonoontinuable power series.
    • COLLATERAL READING
    • 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.
    • COLLATERAL READING
    • 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.
    • COLLATERAL READING
    • 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.
    • COLLATERAL READING
    • 15 NORMAL FAMILIES
    • 15.1. Schwarz's lemma and hyperbolic measure.
    • 15.2. Normal families.
    • 15.3. Induced convergence.
    • 15.4. Applications.
    • COLLATERAL READING
    • 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.
    • COLLATERAL READING
    • 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.
    • COLLATERAL READING
    • 18 MAJORIZATION
    • 18.1. The Phragmen-Lindelof Principle.
    • 18.2. Dirichlet's problem; Lindelof's principle.
    • 18.3. Harmonic measure.
    • 18.4. The Nevanlinna-Ahlfors-Heins theorems.
    • 18.5. Subordination.
    • COLLATERAL READING
    • 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.
    • COLLATERAL READING
    • Bibliography
    • Index
    • Back Cover
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
AMS Chelsea Publishing
Volume: 270; 1962; 496 pp
MSC: Primary 30; 01

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 textbook-treatise, 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 half-plane.
  • Front Cover
  • Foreword
  • Contents
  • Volume I
  • Volume II
  • Symbols
  • 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.
  • COLLATERAL READING
  • 11 SINGULARITIES AND REPRESENTATION OF ANALYTIC FUNCTIONS
  • 11.1. Holomorphy-preserving transformations: I. Integral operators.
  • 11.2. Holomorphy-preserving transformations: Il. 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 nonoontinuable power series.
  • COLLATERAL READING
  • 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.
  • COLLATERAL READING
  • 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.
  • COLLATERAL READING
  • 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.
  • COLLATERAL READING
  • 15 NORMAL FAMILIES
  • 15.1. Schwarz's lemma and hyperbolic measure.
  • 15.2. Normal families.
  • 15.3. Induced convergence.
  • 15.4. Applications.
  • COLLATERAL READING
  • 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.
  • COLLATERAL READING
  • 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.
  • COLLATERAL READING
  • 18 MAJORIZATION
  • 18.1. The Phragmen-Lindelof Principle.
  • 18.2. Dirichlet's problem; Lindelof's principle.
  • 18.3. Harmonic measure.
  • 18.4. The Nevanlinna-Ahlfors-Heins theorems.
  • 18.5. Subordination.
  • COLLATERAL READING
  • 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.
  • COLLATERAL READING
  • Bibliography
  • Index
  • Back Cover
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
You may be interested in...
Powered by MathJax
Please select which format for which you are requesting permissions.