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 ...

As we listen to a piece of music, our ears perform a calculation. The high-pitched flutter of the flute, the middle tones of the violin, and the low hum of the double bass fill the air with pressure ...

Lie groups furnish a unifying framework in which group theory and smooth geometry intersect. As smooth manifolds endowed with a group operation that is infinitely differentiable, Lie groups serve as ...