Year: 2026
Type: preprint
Abstract: In this paper, we establish sampling and density results for the fractional Opdam-Cherednik transform. Using the Sturm-Liouville structure of Jacobi functions, we construct a Riesz basis associated with the Opdam-Cherednik kernel and derive an explicit sampling formula. The sampling nodes are determined by the zeros of a shifted Jacobi function. We further develop a concentration-operator approach and obtain Landau-type necessary density conditions for sampling and interpolation in fractional Opdam-Cherednik bandlimited spaces. The non-fractional Opdam-Cherednik sampling formula is recovered when $θ=π/2$.
Source: arXiv (Cornell University)
Authors: Ghosh, Riya, Poria, Anirudha
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G3285182997
OpenAlex ID: W7208722307