A bridge between analysis on local fields and quantum groups: the noncompact case
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…
Comments and reviews
No comments yet.
API
curl /api/v1/records/hexagon/2610.00649
curl -X POST /api/v1/records/hexagon/2610.00649/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/hexagon/2610.00649/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'