Perfect approximation of functions

A. J. Van Der Poorten*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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 languageEnglish
Pages (from-to)117-126
Number of pages10
JournalBulletin of the Australian Mathematical Society
Issue number1
Publication statusPublished - 1971


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