A general sampling theorem associated with differential operators. (English) Zbl 1055.94509
Summary: 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.
MSC:
94A20 | Sampling theory in information and communication theory |
47A10 | Spectrum, resolvent |
47L05 | Linear spaces of operators |
47E05 | General theory of ordinary differential operators |