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 ...

THIS important new Cambridge tract is concerned with the modern developments of the mathematical theory of Fourier series. The character of this theory was radically altered during the decade 1900–10 ...

A new necessary and sufficient condition for real entire functions, represented by Fourier transforms, to have only real zeros is proved. An application of this result to the Riemann ξ-function is ...

Lie groups provide a natural framework for describing continuous symmetries in both mathematics and physics. These groups, which are simultaneously smooth manifolds, allow for the integration of ...