We define the class of integral holomorphic functions over Banach spaces; these are functions admitting an integral representation akin to the Cauchy integral formula, and are related to integral polynomials. After studying various properties of these functions, Banach and Fréchet spaces of integral holomorphic functions are defined, and several aspects investigated: duality, Taylor series approximation, biduality and reflexivity.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm160-1-4,
author = {Ver\'onica Dimant and Pablo Galindo and Manuel Maestre and Ignacio Zalduendo},
title = {Integral holomorphic functions},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {83-99},
zbl = {1055.46025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm160-1-4}
}
Verónica Dimant; Pablo Galindo; Manuel Maestre; Ignacio Zalduendo. Integral holomorphic functions. Studia Mathematica, Tome 162 (2004) pp. 83-99. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm160-1-4/