Best approximation by polynomials

Sung Guen Kim

doi:10.1017/s0004972700037643

Best approximation by polynomials

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Abstract

In this paper we show that if E is a separable Banach space, F is a reflexive Banach space, and n, k ∈ ℕ, then every continuous polynomial of degree n from E into F has at least one element of best approximation in the Banach subspace of all continuous k-homogeneous polynomials from E into F.

Original language	English
Pages (from-to)	267-273
Number of pages	7
Journal	Bulletin of the Australian Mathematical Society
Volume	68
Issue number	2
DOIs	https://doi.org/10.1017/s0004972700037643
State	Published - Oct 2003

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10.1017/s0004972700037643

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abstract = "In this paper we show that if E is a separable Banach space, F is a reflexive Banach space, and n, k ∈ ℕ, then every continuous polynomial of degree n from E into F has at least one element of best approximation in the Banach subspace of all continuous k-homogeneous polynomials from E into F.",

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Best approximation by polynomials

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