COMPLEX ANALYSIS IN ONE AND SEVERAL VARIABLES

Complex Dynamics in Several Variables

1. Motivation 117 2. Iteration of Maps 118 3. Regular Versus Chaotic Behavior 119 4. The Horseshoe Map and Symbolic Dynamics 120 5. Hénon Maps 123 6. Properties of Horseshoe and Hénon Maps 126 7. Dynamically Defined Measures 127 8. Potential Theory 129 9. Potential Theory in One-Variable Dynamics 131 10. Potential Theory and Dynamics in Two Variables 133 11. Currents and Applications to Dynamic...

Outer Factorizations in One and Several Variables

A multivariate version of Rosenblum’s Fejér-Riesz theorem on outer factorization of trigonometric polynomials with operator coefficients is considered. Due to a simplification of the proof of the single variable case, new necessary and sufficient conditions for the multivariable outer factorization problem are formulated and proved.

Complex Scaling and Geometric Analysis of Several Variables

It is a classical fact that there is no Riemann mapping theorem in the function theory of several complex variables. Indeed, H. Poincaré proved in 1906 that the unit ball B = {z = (z1, z2) ∈ C 2 : |z| ≡ |z1| 2 + |z2| 2 < 1} and the unit bidisc D = {z = (z1, z2) ∈ C 2 : |z1| < 1, |z2| < 1} are biholomorphically inequivalent. More recently, Burns/Shnider/Wells [BSW] and Greene/Krantz [GRK1] have ...

Several Complex Variables and Analytic Spaces

D’Angelo, John P. Inequalities from complex analysis. (English summary) 2003e:32001 Fritzsche, Klaus (with Grauert, Hans) From holomorphic functions to complex manifolds. (English summary) 2003g:32001 Grauert, Hans see Fritzsche, Klaus, 2003g:32001 (Nakamura, Shu Gilbert) see Ohsawa, Takeo, 2003d:32001 Ohsawa, Takeo Analysis of several complex variables. (English summary) 2003d:32001 Range, R. ...

Composition Operators and Several Complex Variables