Analytic Kramer Sampling and Quasi Lagrange-Type Interpolation in Vector Valued RKHS

This paper discusses an abstract Kramer sampling theorem for functions within a reproducing kernel Hilbert space (RKHS) of vector valued holomorphic functions. Additionally, we extend the concept of quasi Lagrange-type interpolation for functions within a RKHS of vector valued entire functions. The dependence of having quasi Lagrange-type interpolation on an invariance condition under the generalized backward shift operator has also been discussed. Furthermore, the paper establishes the connection between quasi Lagrange-type interpolation, operator of multiplication by the independent variable, and de Branges spaces of vector valued entire functions.