发表机构
Indian Institute of Technology Bombay; Xi’an Jiaotong-Liverpool University（印度孟买理工学院; 西交利物浦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对分数阶Opdam-Cherednik变换，利用雅可比函数结构构造Riesz基推导采样公式，发展集中算子方法得到密度条件，θ=π/2时可恢复非分数阶对应公式，建立了相关采样与密度理论结果。
AI 中文摘要
本文针对分数阶Opdam-Cherednik变换建立了采样与密度结果。利用雅可比函数的Sturm-Liouville结构，构造了与Opdam-Cherednik核相关的Riesz基，并推导了显式采样公式，采样节点由移位雅可比函数的零点确定。进一步发展了集中算子方法，得到分数阶Opdam-Cherednik带限空间中采样与插值的Landau型必要密度条件，当θ=π/2时可恢复非分数阶Opdam-Cherednik采样公式。
英文摘要
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 $θ=π/2$.
Comments33 pages
