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Starting from Lagrange interpolation of the exponential function in the complex plane, and using an integral representation formula for holomorphic functions on Banach spaces, we obtain Lagrange interpolating polynomials for representable functions defined on a Banach space . Given such a representable entire funtion , in order to study the approximation problem and the uniform convergence of these polynomials to on bounded sets of , we present a sufficient growth condition on the interpolating...
We show that if U is a domain of existence in a separable Banach space, then the set of holomorphic functions on U whose domain of existence is U is lineable and algebrable.
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.
It is shown that if E is a Frechet space with the strong dual E* then Hb(E*), the space of holomorphic functions on E* which are bounded on every bounded set in E*, has the property (DN) when E ∈ (DN) and that Hb(E*) ∈ (Ω) when E ∈ (Ω) and either E* has an absolute basis or E is a Hilbert-Frechet-Montel space. Moreover the complementness of ideals J(V) consisting of holomorphic functions on E* which are equal to 0 on V in H(E*) for every nuclear Frechet space E with E ∈ (DN) ∩ (Ω) is stablished...
Estudiamos algunas situaciones donde encontramos un problema que, a primera vista, parece no tener solución. Pero, de hecho, existe un subespacio vectorial grande de soluciones del mismo.
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