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 ...

Amid the chaos of revolutionary France, one man’s mathematical obsession gave way to a calculation that now underpins much of mathematics and physics. The calculation, called the Fourier transform, ...

It is now possible to calculate the Fourier transform of an image on your smartphone, thanks to a new app developed by two nanophotonics researchers in The Netherlands. “2D-Fourier” is available for ...

We study certain Hilbert transforms and maximal functions along variable flat curves in the plane. We obtain their L 2 (R 2) boundedness by considering the oscillatory singular integrals which arise ...