Lagrange approximation in Banach spaces

Czechoslovak Mathematical Journal

Lisa ¹  Nilsson² 

[1] If P&C Insurance, Barks vg 15, SE-10680 Stockholm, Sweden;Ignacio Zalduendo, Universidad T. Di Tella, Av. Figueroa Alcorta 7350 (C1428BCW), Buenos Aires, Argentina

关键词: Lagrange interpolation;    Lagrange approximation;    Kergin interpolation;    Kergin approximation;    Banach space;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

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 $fE \to\mathbb C$, 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 sequence.

【 授权许可】

Unknown