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Algebras of holomorphic functions with Hadamard multiplication

Hermann Render; Andreas Sauer — 1996

Studia Mathematica

A systematic investigation of algebras of holomorphic functions endowed with the Hadamard product is given. For example we show that the set of all non-invertible elements is dense and that each multiplicative functional is continuous, answering some questions in the literature.

Invariance properties of homomorphisms on algebras of holomorphic functions with the Hadamard product

Hermann Render; Andreas Sauer — 1996

Studia Mathematica

Let $H (G_{1})$ be the set of all holomorphic functions on the domain $G_{1} .$ Two domains $G_{1}$ and $G_{2}$ are called Hadamard-isomorphic if $H (G_{1})$ and $H (G_{2})$ are isomorphic algebras with respect to the Hadamard product. Our main result states that two admissible domains are Hadamard-isomorphic if and only if they are equal.

Meromorphic functions with shared limit values.

Sauer, Andreas — 2002

Annales Academiae Scientiarum Fennicae. Mathematica

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Algebras of holomorphic functions with Hadamard multiplication

Invariance properties of homomorphisms on algebras of holomorphic functions with the Hadamard product

Meromorphic functions with shared limit values.