Perfect approximation of functions
- 1 August 1971
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 5 (1) , 117-126
- https://doi.org/10.1017/s0004972700046931
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.Keywords
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