When last we saw [xoreaxeax], he had built a lens-less optical microscope that deduced the structure of a sample by recording ...

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 ...

Fourier analysis and numerical methods have long played a pivotal role in the solution of differential equations across science and engineering. By decomposing complex functions into sums of ...

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 ...

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 ...

BELLINGHAM, Washington, USA - Joe Goodman, an international expert in Fourier optics, statistical optics, and speckle phenomena, has published his latest book, Fourier Transforms Using Mathematica®, ...

FFT-EM is an innovative method that represents a combination of FFT and EM techniques such as scanning electron microscopy (SEM). The technique is often used to determine the interior and surface ...

Let f(u) be the Fourier-Stieltjes transform of a real or complex-valued function F(α) of bounded variation on (— ∞, ∞). It is shown that if f(u) belongs to L2 on an interval of infinite range, then ...