Amid the chaos of revolutionary France, one man’s mathematical obsession gave way to a calculation that now underpins much of ...

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 ...

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, ...

Although examples have been given showing that the spherical average of the Fourier transform cannot decay always too fast, they usually do not exhibit a single measure decaying sufficiently slow on ...