The analytic wave-front set of distributions and the F.B.I. transform | Colóquio do DFMA

The analytic wave-front set describes the points in the "phase-space" where a given distribution "fails to be real-analytic". This concept is not only interesting from the mathematical point of view, but it also links to causality (which I'll not discuss in detail in this talk). In this talk I'll recall the definitions of the wave-front set of distributions, and then give a characterization of it in terms of boundary values of holomorphic function on wedges. Then, we'll use this characterization to motivate the definition of the analytic wave-front set, and present a characterization via the decay of the so-called Fourier-Bros-Iagolnitzer transform (or F.B.I. transform).

Confira em: https://www.youtube.com/@dfmaifusp/streams