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A General Sampling Theorem Associated with Differential Operators (1999)

García, A. G. ; Hernández-Medina, M. A.

Springer

Journal of computational analysis and applications 1 (1999), S. 147-161

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ISSN: 1572-9206

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

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1022625625116

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