Partial sequences and subsequences of Hamburger moment sequences arise where data have been lost or interpolation is sought. All the relevant questions dealing with full moment sequences, such as positivity and partial positivity, relationship between the corresponding measures and determinacy can be posed for the partial data. In this paper, we characterize the moment subsequences of Hamburger moment sequences, give a description of certain completable patterns of partial sequences and provide a simple relationship between the Cauchy transform of the moment sequence and its moment subsequences. A general result for perturbation of moment sequences by arbitrary sequences is also given.
- Cauchy transform
- Hamburger moment completions
- Hankel matrices
- Moment problems
- perturbation of moment sequences