Projections in the Space H∞ and the Corona Theorem for Coverings of Bordered Riemann Surfaces
نویسنده
چکیده
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).
منابع مشابه
A 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], ...
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