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 ...

Fourier Restriction Theory investigates the conditions under which the Fourier transform of a function, when confined to a geometric surface such as a sphere, paraboloid or other manifold, remains ...

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 ...