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

Hermann Render; Andreas Sauer

Studia Mathematica (1996)

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

Abstract

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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.

How to cite

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Render, 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

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

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