Analytic Function Theory, Volume II

Häftad, Engelska, 1962

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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.

Produktinformation

Utgivningsdatum1962-01-10
Mått152 x 229 x undefined mm
FormatHäftad
SpråkEngelska
SerieAMS Chelsea Publishing
Antal sidor496
FörlagAmerican Mathematical Society
ISBN9780821833445

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Front CoverForewordContentsVolume IVolume IISymbols10 ANALYTIC CONTINUATION10.1. 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 READING11 SINGULARITIES AND REPRESENTATION OF ANALYTIC FUNCTIONS11.1. 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 READING12 ALGEBRAIC FUNCTIONS12.1. Local properties.12.2. Critical points.12.3. Newton's diagram.12.4. Riemann surfacessome concepts of algebraic geometry.12.5. Rational functions on the surface and Abelian integrals.COLLATERAL READING13 ELLIPTIC FUNCTIONS13.1. 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 READING14 ENTIRE AND MEROMORPHIC FUNCTIONS14.1. 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 READING15 NORMAL FAMILIES15.1. Schwarz's lemma and hyperbolic measure.15.2. Normal families.15.3. Induced convergence.15.4. Applications.COLLATERAL READING16 LEMNISCATES16.1. Chebichev polynomials.16.2. The transfinite diameter.16.3. Additive set functionsRadon-Stieltjes integrals.16.4. Logarithmic capacity.16.5. Green's functionHilbert's theorem.16.6. Runge's theorem.16. 7. Overconvergence.COLLATERAL READING17 CONFORMAL MAPPING17.1. 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 READING18 MAJORIZATION18.1. The Phragmen-Lindelof Principle.18.2. Dirichlet's problemLindelof's principle.18.3. Harmonic measure.18.4. The Nevanlinna-Ahlfors-Heins theorems.18.5. Subordination.COLLATERAL READING19 FUNCTIONS HOLOMORPHIC IN A HALF-PLANE19.1. The Hardy-Lebesgue classes.19.2. Bounded functions.19.3. Growth-measuring functions.19.4. Remarks on Laplace-Stieltjes integrals.COLLATERAL READINGBibliographyIndexBack Cover