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.
Soit une courbe de Jordan fermée rectifiable dans le plan de la variable complexe. On dit que véfifie la condition corde-arc sioù est la longueur du plus petit arc de joignant et . Soit une représentation conforme du disque unité dans l’intérieur de . Nous prouvons que restreint à appartient à la classe de Muckenhoupt et nous en tirons certains corollaires. Dans deux cas particuliers nous montrons que le résultat peut être amélioré.
Let be the set of all holomorphic functions on the domain Two domains and are called Hadamard-isomorphic if and 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.
n the present paper the authors study some families of functions from a complex linear space into a complex linear space . They introduce the notion of -symmetrical function (; ) which is a generalization of the notions of even, odd and -symmetrical functions. They generalize the well know result that each function defined on a symmetrical subset of can be uniquely represented as the sum of an even function and an odd function.