Kramer-type sampling theorems associated with higher-order differential equations

Abstract For many decades, Kramer’s sampling theorem has been attracting enormous interest in view of its important applications various branches. In this paper we present a new approach to Kramer-type theory based on spectral differential equations higher order an interval the real line. Its novelty relies partly fact that corresponding eigenfunctions are orthogonal with respect scalar product involving classical measure together point mass at finite endpoint domain. particular, is established, which associated self-adjoint Bessel-type boundary value problem fourth-order [0, 1]. Moreover, consider Laguerre and Jacobi their higher-order generalizations establish Green-type formulas operators as essential key towards theory.