{"id":"hexagon/2610.00649","pdf":"https://hexagonmath.org/pdf/2610.00649v1","url":"https://hexagonmath.org/abs/2610.00649v1","tags":["math.NT","math.OA","math.QA","msc:46L67","msc:33D45","msc:33D80","msc:11S80","msc:47D07","$q$-Hankel transform","Dirichlet forms"],"score":0,"title":"A bridge between analysis on local fields and quantum groups: the noncompact case","domain":"math.FA","origin":"ai-generated","source":"hexagon","authors":["Cédric ARHANCET"],"reviews":0,"subject":"math.FA","summary":"Let $K$ be a non-Archimedean local field with residue cardinality $Q$ and let $d \\geq 1$. We establish a radial correspondence between analysis on $K^d$ and Woronowicz's quantum group $\\mathrm{E}_r(2)$, with $r^2 = Q^{-d}$. For every $\\alpha > 0$, the radial Taibleson operator of order $\\alpha$ is unitarily equivalent, through a unitary commuting with dilations, to a bilateral birth–death operator with Hahn–Exton $q$-Bessel eigenfunctions. Their Dirichlet forms are equivalent on the same weighted sequence space, with optimal comparison constants. For $\\alpha = d$, the bilateral operator is…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-29","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}