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Differentiate And Make Waves, R. Nillsen

Faculty of Informatics - Papers (Archive)

In 1972 Gary Meisters and Wolfgang Schmidt showed that if the Fourier coefficient of a function is zero at the origin, then the function is a sum of three first order differences. They deduced from this that every translation invariant linear form on the space of square integrable functions on the circle group is automatically continuous. Their results were subsequently developed by the author for the case of n-dimensional Euclidean space (Lectures Notes in Mathematics, vol. 1586, Springer-Verlag,1994). The present paper gives an exposition of some of the ideas in this work, with the aim of minimising the technicalities. In …