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Lagrange approximation in Banach spaces

Lisa Nilsson, Damián Pinasco, Ignacio M. Zalduendo (2015)

Czechoslovak Mathematical Journal

Starting from Lagrange interpolation of the exponential function e z 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 E . Given such a representable entire funtion f : E → ℂ , in order to study the approximation problem and the uniform convergence of these polynomials to f on bounded sets of E , we present a sufficient growth condition on the interpolating...

Lineability of the set of holomorphic mappings with dense range

Jerónimo López-Salazar (2012)

Studia Mathematica

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.

Linear topological invariants of spaces of holomorphic functions in infinite dimension.

Nguyen Minh Ha, Le Mau Hai (1995)

Publicacions Matemàtiques

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...

Linearity in non-linear problems.

Richard Aron, Domingo García, Manuel Maestre (2001)

RACSAM

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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