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Kergin interpolation in Banach spaces

Henrik Petersson (2002)

Studia Mathematica

We study the Kergin operator on the space H N b ( E ) of nuclearly entire functions of bounded type on a Banach space E. We show that the Kergin operator is a projector with interpolating properties and that it preserves homogeneous solutions to homogeneous differential operators. Further, we show that the Kergin operator is uniquely determined by these properties. We give error estimates for approximating a function by its Kergin polynomial and show in this way that for any given bounded sequence of interpolation...

Kneser-type theorem for the Darboux problem in Banach spaces

Mieczysław Cichoń, Ireneusz Kubiaczyk (2001)

Commentationes Mathematicae Universitatis Carolinae

In this paper we study the Darboux problem in some class of Banach spaces. The right-hand side of this problem is a Pettis-integrable function satisfying some conditions expressed in terms of measures of weak noncompactness. We prove that the set of all local pseudo-solutions of our problem is nonempty, compact and connected in the space of continuous functions equipped with the weak topology.

La théorie des cônes biréticulés

Alain Goullet de Rugy (1971)

Annales de l'institut Fourier

Soient 𝒮 la classe des cônes convexes saillants faiblement complets et 𝒮 loc la sous-classe de 𝒮 formée des cônes localement compacts de 𝒮 . Dans les dix dernières années, Alfsen, Bauer, Effros, Rogalski et Stormer ont donné de nombreuses propriétés équivalentes entre elles et qui caractérisent dans 𝒮 loc les cônes de Radon 𝔐 + ( T ) des mesures de Radon positives sur un espace compact T . On montre ici que ces propriétés, convenablement interprétées, restent équivalentes dans la sous-classe 𝒮 p b c des cônes presque bien...

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...

Lattice-valued Borel measures. III.

Surjit Singh Khurana (2008)

Archivum Mathematicum

Let X be a completely regular T 1 space, E a boundedly complete vector lattice, C ( X ) ( C b ( X ...

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