Corona Theorem for H∞ on Coverings of Riemann Surfaces of Finite Type
نویسنده
چکیده
In this paper continuing our work started in [Br1]-[Br3] we prove the corona theorem for the algebra of bounded holomorphic functions defined on an unbranched covering of a Caratheodory hyperbolic Riemann surface of finite type.
منابع مشابه
Projections in the Space H∞ and the Corona Theorem for Coverings of Bordered Riemann Surfaces
Let M be a non-compact connected Riemann surface of finite type, and R ⊂⊂ M be a relatively compact domain such that H1(M,Z) = H1(R,Z). Let R̃ −→ R be a covering. We study the algebra H∞(U) of bounded holomorphic functions defined in some domains U ⊂ R̃. Our main result is a Forelli type theorem on projections in H∞(D).
متن کاملExtension of Matrices with Entries in H∞ on Coverings of Riemann Surfaces of Finite Type
The paper continues an earlier work of the author. An extension theorem is proved for matrices with entries in the algebra of bounded holomorphic functions defined on an unbranched covering of a Carathéodory hyperbolic Riemann surface of finite type.
متن کاملAn extension theorem for finite positive measures on surfaces of finite dimensional unit balls in Hilbert spaces
A consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable Hilbert space. It is proved, through a Kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the Hilbert space. As an application, this will naturally accomplish the work of Kante...
متن کاملA New Construction of Riemann Surfaces with Corona
equivalently [Gar,VIII.2], the corona M(X) \ ι(X) is empty. (Here M(X) is the maximal ideal space of the algebra H∞(X) of bounded holomorphic functions on X and ι is the natural inclusion X ↪→ M(X).) If X does not satisfy the corona theorem then X may be said to have corona. Riemann surfaces known to satisfy the corona theorem include the unit disk [Car], bordered Riemann surfaces [All] [Sto], ...
متن کاملRamified Coverings of the Riemann Sphere, Constellations, and Hypermaps on Surfaces
We review the theory of compact Riemann surfaces and connections between ramified coverings of the Riemann sphere, constellations, and hypermaps on surfaces. This note is based on the chapter 1 of [4].
متن کامل