Appears in collection : 2025 - T1 - WS1 - Intertwining operators and geometry

In recent years, an analytical framework based on the “$(k,a)$-generalized Fourier analysis” introduced by Ben Saîd--Kobayashi--Ørsted has been actively studied. This is a novel branch of harmonic analysis that deforms the traditional Fourier analysis theory using two parameters, $k$ and $a$, arising from Dunkl theory and the interpolation theory of minimal representations of Lie groups. In this talk, I will introduce what is currently known about how concepts related to harmonic analysis, such as the heat equation, heat kernel, and Brownian motion, are able to be generalized in this new framework and what fundamental properties they have.