In this paper, we prove an exponential integral formula for the Fourier transform of Bessel functions over complex numbers, along with a radial exponential integral formula. The former will enable us ...

Harmonic analysis occupies a central position in modern mathematical analysis by providing the tools to express complex functions as superpositions of simpler sinusoidal components via the Fourier ...

In this article we will study the spectral properties of a deterministic signal exponentially damped in the past and in the future (the damping in the future is controlled by a time constant). The ...

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 ...

When it comes to mathematics, the average person can probably get through most of life well enough with just basic algebra. Some simple statistical concepts would be helpful, and a little calculus ...

In less than 100 seconds, Carola-Bibiane Schönlieb of the University of Cambridge in the UK provides a basic definition of a Fourier transform. She explains how this mathematical tool was introduced ...

Over at Quanta Magazine [Shalma Wegsman] asks What Is the Fourier Transform? [Shalma] begins by telling you a little about Joseph Fourier, the French mathematician with an interest in heat propagation ...