1. MUSA SIDDIG - University of Kordofan, Faculty of Science, Department of Mathematics, Sudan.
2. AMANI ELSEID ABUZEID - Department of Mathematics, College of Aldaier, Jazan University, Saudi Arabia.
When a function’s values are located in a separable Hilbert space, it is derived the Whittaker-Shannon- Kotel ′nikov sampling theorem. During a Hilbert space, we employ small frame operators and frames. In turn, this provides us an extension Kramer’s second sampling theorem and helps us grow selection of
theorems related to value at the boundary issues and various formulae for homogeneous integrals.
Theorem Of Shannon s Sampling, Approximation And Interpolation In A Hilbert Space, Frame Operators And Frames, Sturm-Liouville Boundary-Value Problem, Fredholm Integral Equations, Green s Function, Cauchy-Schwarz Inequality.