Every non-zero complex homomorphism of the almost periodic functions on an abelian group is induced by the Fourier transform. A Plancherel formula for almost periodic functions and a necessary ...

We obtain exponentially accurate Fourier series for nonperiodic functions on the interval [−1, 1] by extending these functions to periodic functions on a larger domain. The series may be evaluated, ...

A mathematical theorem stating that a PERIODIC function f(x) which is reasonably continuous may be expressed as the sum of a series of sine or cosine terms (called the Fourier series), each of which ...

THE theory of functions of a real variable is a subject of fairly recent date and is necessarily expanding as new theorems are discovered and fresh generalisations effected. On the other hand, the ...