Sampling theorems for Jackson-Nörlund transforms associated with Hahn-difference operators
A \(q,\omega\)-Hahn Sturm-Liouville theory is established in the work [\textit{M. H. Annaby} et al., Contemp. Math. Appl., Monogr. Expo. Lect. Notes 1, 35--83 (2018; Zbl 1415.39014)]. In this paper, the authors derive sampling theorems for the same \(q,\omega\)-Sturm-Liouville problem. The \(q,\omega\)-Hahn difference operator approximates the classical derivative as \(q\rightarrow 1^{-}\) and \(\omega \rightarrow 0^{+}\). Therefore, the authors give a few numerical examples for the sampling representation, indicating that this approximation.
scientific article; zbMATH DE number 6867359