On a Symbolic Proof of Fourier’s Theorem

Extract

Some time ago, when attempting to generalise certain methods of solving differential equations by operators, the writer came across the following mode of deducing Fourier’s Theorem symbolically.

The method is so simple that it seems improbable that it should be unknown. The nearest approach to it known to the author, however, occurs in Oliver Heaviside’s Electromagnetic Theory, Vol. II. §§ 275 et seq., but the investigation there proceeds on somewhat different lines, and the interpretation of the operators used requires to be carefully defined.