Author | Andersson, Mats. author |
---|---|
Title | Topics in Complex Analysis [electronic resource] / by Mats Andersson |
Imprint | New York, NY : Springer New York, 1997 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4042-6 |
Descript | VIII, 157 p. online resource |
Preliminaries -- ยง1. Notation -- ยง2. Some Facts -- 1. Some Basic Properties of Analytic Functions -- ยง1. Definition and Integral Representation -- ยง2. Power Series Expansions and Residues -- ยง3. Global Cauchy Theorems -- 2. Properties of Analytic Mappings -- ยง1. Conformal Mappings -- ยง2. The Riemann Sphere and Projective Space -- ยง3. Univalent Functions -- ยง4. Picardโs Theorems -- 3. Analytic Approximation and Continuation -- ยง1. Approximation with Rationals -- ยง2. Mittag-Lefflerโs Theorem and the Inhomogeneous Cauchy-Riemann Equation -- ยง3. Analytic Continuation -- ยง4. Simply Connected Domains -- ยง5. Analytic Functionals and the Fourier-Laplace Transform -- ยง6. Mergelyanโs Theorem -- 4. Harmonic and Subharmonic Functions -- ยง1. Harmonic Functions -- ยง2. Subharmonic Functions -- 5. Zeros, Growth, and Value Distribution -- ยง1. Weierstrassโ Theorem -- ยง2. Zeros and Growth -- ยง3. Value Distribution of Entire Functions -- 6. Harmonic Functions and Fourier Series -- ยง1. Boundary Values of Harmonic Functions -- ยง2. Fourier Series -- 7. IF Spaces -- ยง1. Factorization in Hp Spaces -- ยง2. Invariant Subspaces of H2 -- ยง3. Interpolation of H? -- ยง4. Carleson Measures -- 8. Ideals and the Corona Theorem -- ยง1. Ideals in A(?) -- ยง2. The Corona Theorem -- 9. H1 and BMO -- ยง1. Bounded Mean Oscillation -- ยง2. The Duality of H1 and BMO -- List of Symbols