Toeplitz operators in several complex variables

Composition Operators and Several Complex Variables

Hankel Operators in Several Complex Variables and Product Bmo

H(⊗1 C+) denotes the Hardy space of square integrable functions analytic in each variable separately. Let P be the natural projection of L(⊗1 C+) onto H (⊗1 C+). A Hankel operator with symbol b is the linear operator from H(⊗1 C+) to H (⊗1 C+) given by Hb φ = P⊖bφ. We show that ‖Hb‖ ≃ ‖P b‖BMO(⊗n 1 C+) , where the right hand norm is S.-Y. Chang and R. Fefferman product BMO. This fact has well k...

Factorization of Almost Periodic Matrix Functions of Several Variables and Toeplitz Operators

We study connections between operator theoretic properties of Toeplitz operators acting on suitable Besikovitch spaces and factorizations of their symbols which are matrix valued almost periodic functions of several real variables. Among other things, we establish the existence of a twisted canonical factorization for locally sectorial symbols, and characterize one-sided invertibility of Toepli...

Power Bounded Composition Operators in Several Variables

Let φ be an analytic self-map of the open unit polydisk D , N ∈ N. Such a map induces a composition operator Cφ acting on weighted Banach spaces of holomorphic functions. We study when such operators are power bounded resp. uniformly mean ergodic. Mathematics Subject Classification (2010): 47B33, 47B38

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...