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Perfect approximation of functions

Published online by Cambridge University Press:  17 April 2009

A.J. van der Poorten
A.J. van der Poorten
Affiliation:
The University of New South Wales, Kensington, New South Wales.
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 5 , Issue 1 , August 1971 , pp. 117 - 126
Copyright
Copyright © Australian Mathematical Society 1971

References

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