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Let f be a holomorphic function on a complex normed space E. The possibility of extending f to the completion of E has been studied by Hirschowitz, Noverraz, Dineen, and Dineen-Noverraz. Here, following the ideas in [4, section 6.1], we study th[...]texto impreso
Let f be a holomorphic function on a complex normed space E. The possibility of extending f to the completion of E has been studied by Hirschowitz, Noverraz, Dineen, and Dineen-Noverraz. Here, following the ideas in [4, section 6.1], we study th[...]texto impreso
Ansemil, José María M. ; López-Salazar Codes, Jerónimo ; Ponte, Socorro | Polish Acad Sciencies Inst Mathematics | 2011Let X be an infinite-dimensional complex Banach space. Very recently, several results on the existence of entire functions on X bounded on a given ball B(1) subset of X and unbounded on another given ball B(2) subset of X have been obtained. In [...]texto impreso
El espacio H(U) de funciones holomorfas en un abierto U del plano complejo ha sido siempre uno de los ejemplos clásicos en la teoría de espacios localmente convexos. Con la topología compacto-abierta, H(U) es metrizable, completo, tonelado, born[...]texto impreso
In this paper we prove several results on the existence of analytic functions on an infinite dimensional real Banach space which are bounded on some given collection of open sets and unbounded on others. In addition, we also obtain results on th[...]texto impreso
Ansemil, José María M. ; Ponte, Socorro ; López-Salazar Codes, Jerónimo | European Mathematical Society | 2015This paper is devoted to studying the space A(U) of all analytic functions on an open subset U of ?? or ??. It is proved that if U satisfies a weak condition (that will be called the 0-property), then every f ? A(U) depends only on afinite numbe[...]
