06-204 Luis O. Silva and Julio H. Toloza

Applications of M.G. Krein's Theory of Regular Symmetric Operators to Sampling Theory (43K, LaTeX 2e ) Jul 17, 06

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Abstract. The classical Kramer sampling theorem establishes general conditions that allow the reconstruction of functions by orthogonal sampling formulas. One major task in sampling theory is to find concrete, non trivial realizations of this theorem. In this paper we provide a new approach to this subject on the basis of the M. G. Krein's theory of simple regular symmetric operators, with deficiency indices $(1,1)$, for obtaining Kramer-type sampling formulas. We show that these formulas have the form of Lagrange interpolation series. Concerning the case of entire operators, we also characterize the space of functions reconstructible by our sampling formulas.

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