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Sampling and Density Theorems for the Fractional Opdam-Cherednik Transform

  • Riya Ghosh
  • Anirudha Poria
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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.

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Cite

BibTeXRIS
BibTeX
@misc{ghosh2026sampling,
  title = {{Sampling and Density Theorems for the Fractional Opdam-Cherednik Transform}},
  author = {Riya Ghosh and Anirudha Poria},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03418},
  eprint = {2609.03418},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03418},
}
RIS
TY  - UNPB
TI  - Sampling and Density Theorems for the Fractional Opdam-Cherednik Transform
AU  - Riya Ghosh
AU  - Anirudha Poria
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03418
UR  - https://arxiv.org/abs/2609.03418
AB  - 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.
ER  -