Author | Rodin, Burton. author |
---|---|
Title | Principal Functions [electronic resource] / by Burton Rodin, Leo Sario |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1968 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-8038-2 |
Descript | XVIII, 348 p. 1 illus. online resource |
Introduction: What are Principal Functions? -- 0 Prerequisite Riemann Surface Theory -- ยง1. Topology of Riemann Surfaces -- ยง2. Analysis on Riemann Surfaces -- I The Normal Operator Method -- ยง1. The Main Existence Theorem -- ยง2. Normal Operators -- ยง3. The Principal Functions p0 and p1 -- ยง4. Special Topics -- II Principal Functions -- ยง1. Main Extremal Theorem -- ยง2. Conformal Mapping -- ยง3. Reproducing Differentials -- ยง4. Interpolation Problems -- ยง5. The Theorems of Riemann-Roch and Abel -- ยง6. Extremal Length -- III Capacity Stability and Extremal Length -- ยง1. Generalized Capacity Functions -- ยง2. Extremal Length -- ยง3. Exponential Mappings of Plane Regions -- ยง4. Stability -- IV Classification Theory -- ยง1. Inclusion Relations -- ยง2. Other Properties of the O-Classes -- V Analytic Mappings -- ยง1. The Proximity Function -- ยง2. Analytic Mappings -- ยง3. Meromorphic Functions -- VI Principal Forms and Fields on Riemannian Spaces -- ยง1. Principal Functions on Riemannian Spaces -- ยง2. Principal Forms on Locally Flat spaces -- ยง3. Principal Forms on Riemannian Spaces -- VII Principal Functions on Harmonic Spaces -- ยง1. Harmonic Spaces -- ยง2. Harmonic Functions with General Singularities -- ยง3. General Principal Function Problem -- Appendix Sario Potentials on Riemann Surfaces -- ยง1. Continuity Principle -- ยง2. Maximum Principle -- Author Index