For a family of fractal measures, we find an explicit Fourier duality. The measures in the pair have compact support in ℝ d , and they both have the same matrix scaling; but the two use different ...

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 ...

Lie groups provide a natural framework for describing continuous symmetries in both mathematics and physics. These groups, which are simultaneously smooth manifolds, allow for the integration of ...