Abstract.
The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. A challenging problem is to characterize the situations when these sampling formulas can be written as Lagrange-type interpolation series. This article gives a necessary and sufficient condition to ensure that when the sampling formula is associated with an analytic Kramer kernel, then it can be expressed as a quasi Lagrange-type interpolation series; this latter form is a minor but significant modification of a Lagrange-type interpolation series. Finally, a link with the theory of de Branges spaces is established.
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Received: October 8, 2007. Revised: December 13, 2007.
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Everitt, W.N., García, A.G. & Hernández-Medina, M.A. On Lagrange-Type Interpolation Series and Analytic Kramer Kernels. Result. Math. 51, 215–228 (2008). https://doi.org/10.1007/s00025-007-0271-3
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DOI: https://doi.org/10.1007/s00025-007-0271-3