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, ...

Definition: Fourier Transform Infrared (FTIR) Spectroscopy is a highly specialized type of IR spectroscopy. It's the most common way IR measurements are carried out today. FTIR is known for its speed, ...

Many authors have studied the rate of average decay of the Fourier transform of measures because of its relationship with the Falconer’s conjecture. Although examples have been given showing that the ...

We obtain necessary and sufficient conditions on weights for the generalized Fourier-type transforms to be bounded between weighted 𝐿𝑝-𝐿𝑞 spaces. As an important example, we investigate transforms ...