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

Studia Mathematica (1996)

- Volume: 121, Issue: 1, page 53-65
- ISSN: 0039-3223

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topRender, Hermann, and Sauer, Andreas. "Invariance properties of homomorphisms on algebras of holomorphic functions with the Hadamard product." Studia Mathematica 121.1 (1996): 53-65. <http://eudml.org/doc/216342>.

@article{Render1996,

abstract = {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.},

author = {Render, Hermann, Sauer, Andreas},

journal = {Studia Mathematica},

keywords = {Hadamard product; $B_0$-algebras; homomorphisms; -algebras; Hadamard-isomorphic; isomorphic algebras with respect to the Hadamard product},

language = {eng},

number = {1},

pages = {53-65},

title = {Invariance properties of homomorphisms on algebras of holomorphic functions with the Hadamard product},

url = {http://eudml.org/doc/216342},

volume = {121},

year = {1996},

}

TY - JOUR

AU - Render, Hermann

AU - Sauer, Andreas

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

JO - Studia Mathematica

PY - 1996

VL - 121

IS - 1

SP - 53

EP - 65

AB - 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.

LA - eng

KW - Hadamard product; $B_0$-algebras; homomorphisms; -algebras; Hadamard-isomorphic; isomorphic algebras with respect to the Hadamard product

UR - http://eudml.org/doc/216342

ER -

## References

top- [1] L. Bieberbach, Analytische Fortsetzung, Ergeb. Math. Grenzgeb. 3, Springer, Berlin, 1955.
- [2] R. M. Brooks, A ring of analytic functions, Studia Math. 24 (1964), 191-210. Zbl0199.46201
- [3] R. Brück and J. Müller, Invertible elements in a convolution algebra of holomorphic functions, Math. Ann. 294 (1992) 421-438. Zbl0769.30002
- [4] R. Brück and J. Müller, Closed ideals in a convolution algebra of holomorphic functions, Canad. J. Math. 47 (1995), 915-928. Zbl0836.30002
- [5] J. Müller, The Hadamard multiplication theorem and applications in summability theory, Complex Variables 18 (1992), 75-81.
- [6] R. Remmert, Funktionentheorie II, Springer, Berlin, 1991.
- [7] H. Render, Homomorphisms on Hadamard algebras, Rend. Circ. Mat. Palermo Suppl. 40 (1996), 153-158.
- [8] H. Render and A. Sauer, Algebras of holomorphic functions with Hadamard multiplication, Studia Math. 118 (1996), 77-100.

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