Perfect approximation of functions

A. J. Van Der Poorten

doi:10.1017/S0004972700046931

Perfect approximation of functions

A. J. Van Der Poorten^*

^*Corresponding author for this work

Macquarie University Administration Unit

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

There are only isolated instances of vectors of functions for which it is possible to obtain an explicit expression for the remainder functions obtained upon approximating by polynomials in the manner described by Mahler in his paper “Perfect systems”, Compositio Math. 19 (1968). We display appropriate identities and point to a pattern amongst these which suggests we should not expect convenient generalization to wider classes of functions. Proofs of perfectness do not require laborious computation but are immediate from the identities given.

Original language	English
Pages (from-to)	117-126
Number of pages	10
Journal	Bulletin of the Australian Mathematical Society
Volume	5
Issue number	1
DOIs	https://doi.org/10.1017/S0004972700046931
Publication status	Published - 1971

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AB - There are only isolated instances of vectors of functions for which it is possible to obtain an explicit expression for the remainder functions obtained upon approximating by polynomials in the manner described by Mahler in his paper “Perfect systems”, Compositio Math. 19 (1968). We display appropriate identities and point to a pattern amongst these which suggests we should not expect convenient generalization to wider classes of functions. Proofs of perfectness do not require laborious computation but are immediate from the identities given.

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Perfect approximation of functions

Abstract

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