A General Sampling Theorem Associated with Differential Operators

Authors: García A.G.¹; Hernández-Medina M.A.²

Source: Journal of Computational Analysis and Applications, Volume 01, Number 2, April 1999 , pp. 147-161(15)

Publisher: Springer

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Abstract:

In this paper we prove a general sampling theorem associated with differential operators with compact resolvent. Thus, we are able to recover, through a Lagrange-type interpolatory series, functions defined by means of a linear integral transform. The kernel of this transform is related with the resolvent of the differential operator. Most of the well-known sampling theorems associated with differential operators are shown to be nothing but limit cases of this result.

Keywords: Kramer's sampling theorem; symmetric and self-adjoint operators; compact resolvents; Hilbert–Schmidt operators; Lagrange-type interpolatory series

Language: English

Document Type: Research article

Affiliations: 1: Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Leganés, Spain 2: Departamento de Matemática Aplicada, E.T.S.I.T., Universidad Politécnica de Madrid, Madrid, Spain

Publication date: 1999-04-01