Harmonic analysis of differential operators in Banach spaces

Harmonic analysis is a set of techniques that allow us to analyse signals in ways that are reminiscent of the decomposition of a sound into harmonics. Applied to audio or video signals, it forms the mathematical basis of digital technology. This proposal aims to develop harmonic analysis in new contexts. This includes boundary value problems (as in medical or geological imaging), as well as stochastic equations, where signals have a random component (as in financial mathematics). Mixing geometric and probabilistic ideas, this proposal will develop innovative analytical tools that can be used to process and forecast such signals.