Fourier and pseudodifferential operators lie at the heart of modern analysis of differential equations. The Fourier transform recasts differential problems into algebraic ones by converting ...

We recall that the Fourier series for periodic functions of time, such as those we discussed on the previous chapter, produce discrete line spectra with non-zero values only at specific frequencies ...

Harmonic analysis examines functions through the lens of oscillatory behaviour and integral transformations. Central to the field are function spaces—structured collections of functions equipped with ...