A General Sampling Theorem Associated with Differential Operators |
| |
| Authors: | A G García M A Hernández-Medina |
| |
| Institution: | (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 |
| |
| 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 |
| 本文献已被 SpringerLink 等数据库收录！ |
|
