Lagrange approximation in Banach spaces

被引：0

作者：

Lisa Nilsson

Damián Pinasco

Ignacio Zalduendo

机构：

[1] If P&C Insurance,

[2] Universidad T. Di Tella,undefined

来源：

Czechoslovak Mathematical Journal | 2015年 / 65卷

关键词：

Lagrange interpolation; Lagrange approximation; Kergin interpolation; Kergin approximation; Banach space; 46G20; 30E10; 30E20;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Starting from Lagrange interpolation of the exponential function ez 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 sequence.

引用

页码：281 / 288

页数：7

共 15 条

[1]

Andersson M.(1991)Complex Kergin interpolation J. Approx. Theory 64 214-225

[2]

Passare M.(1981)Kergin interpolation of entire functions on ℂ Duke Math. J. 48 69-83

[3]

Bloom T.(2005)Divided differences Surv. Approx. Theory 1 46-69

[4]

de Boor C.(2008)Integral representation of holomorphic mappings on fully nuclear spaces J. Math. Anal. Appl. 339 146-152

[5]

Dineen S.(1970)Intégrabilité des vecteurs Gaussiens C. R. Acad. Sci., Paris, Sér. A 270 1698-1699

[6]

Nilsson L.(2004)Kergin interpolation in Banach spaces J. Approx. Theory 127 108-123

[7]

Fernique X.(1997)Complex mean-value interpolation and approximation of holomorphic functions J. Approx. Theory 91 244-278

[8]

Filipsson L.(1878)On the Maclaurin summation formula and interpolating functions C. R. Acad. Sci., Paris, Sér. A 86 466-469

[9]

Filipsson L.(1980)A natural interpolation of J. Approx. Theory 29 278-293

[10]

Genocchi A.(2002) functions Stud. Math. 153 101-114

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