Holomorphic almost periodic functions on coverings of complex manifolds
نویسنده
چکیده
In this paper we discuss some results of the theory of holomorphic almost periodic functions on coverings of complex manifolds, recently developed by the authors. The methods of the proofs are mostly sheaf-theoretic which allows us to obtain new results even in the classical setting of H. Bohr’s holomorphic almost periodic functions on tube
منابع مشابه
Towards Oka-cartan Theory for Algebras of Holomorphic Functions on Coverings of Stein Manifolds I
We develop complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds. This, in particular, includes the results on holomorphic extension from complex submanifolds, corona type theorems, properties of divisors, holomorphic analogs of the Peter-Weyl approximation theorem, Hartogs type theorems, characterization of uniqueness sets. The model examples ...
متن کاملTowards Oka-cartan Theory for Algebras of Holomorphic Functions on Coverings of Stein Manifolds Ii
We establish basic results of complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds (such as algebras of Bohr’s holomorphic almost periodic functions on tube domains or algebras of all fibrewise bounded holomorphic functions arising, e.g., in the corona problem for H). In particular, in this context we obtain results on holomorphic extension fr...
متن کاملTowards Oka-cartan Theory for Algebras of Fibrewise Bounded Holomorphic Functions on Coverings of Stein Manifolds Ii
We establish basic results of complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds (such as algebras of Bohr’s holomorphic almost periodic functions on tube domains or algebras of all fibrewise bounded holomorphic functions arising, e.g., in the corona problem for H∞). In particular, in this context we obtain results on holomorphic extension f...
متن کاملTowards Oka-cartan Theory for Algebras of Fibrewise Bounded Holomorphic Functions on Coverings of Stein Manifolds I
We develop complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds. This, in particular, includes the topics of holomorphic extension from complex submanifolds, corona type theorems, properties of divisors, holomorphic analogs of the Peter-Weyl approximation theorem, Hartogs type theorems, characterization of uniqueness sets. Our model examples c...
متن کاملIntegral Representations of Holomorphic Functions on Coverings of Pseudoconvex Domains in Stein Manifolds
The classical integral representation formulas for holomorphic functions defined on pseudoconvex domains in Stein manifolds play an important role in the constructive theory of functions of several complex variables. In this paper we construct similar formulas for certain classes of holomorphic functions defined on coverings of such domains.
متن کامل