Displaying similar documents to “A Hahn-Banach Theorem for Holomorphic Mappings on Locally Convex Spaces.”

Extending holomorphic maps in infinite dimensions

Bui Dac Tac (1991)

Annales Polonici Mathematici

Similarity:

Studying the sequential completeness of the space of germs of Banach-valued holomorphic functions at a points of a metric vector space some theorems on extension of holomorphic maps on Riemann domains over topological vector spaces with values in some locally convex analytic spaces are proved. Moreover, the extendability of holomorphic maps with values in complete C-spaces to the envelope of holomorphy for the class of bounded holomorphic functions is also established. These results...

Integral holomorphic functions

Verónica Dimant, Pablo Galindo, Manuel Maestre, Ignacio Zalduendo (2004)

Studia Mathematica

Similarity:

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.

Lineability of the set of holomorphic mappings with dense range

Jerónimo López-Salazar (2012)

Studia Mathematica

Similarity:

Let U be an open subset of a separable Banach space. Let ℱ be the collection of all holomorphic mappings f from the open unit disc 𝔻 ⊂ ℂ into U such that f(𝔻) is dense in U. We prove the lineability and density of ℱ in appropriate spaces for different choices of U.