Mathematics – Classical Analysis and ODEs
Scientific paper
2012-03-27
Mathematics
Classical Analysis and ODEs
Scientific paper
The well-known theorems of Stieltjes, Hamburger and Hausdorff establish conditions on infinite sequences of real numbers to be moment sequences. Further, works by Carath\'{e}odory, Schur and Nevanlinna connect moment problems to problems in function theory and functions belonging to various spaces. In many problems associated with realization of a signal or an image, data may be corrupt or missing. Reconstruction of a function from moment sequences with missing terms is an interesting problem leading to advances in image and/or signal reconstruction. It is easy to show that a subsequence of a moment sequence may not be a moment sequence. Conditions are obtained to show how rigid the space of sub-moment sequences is and necessary and sufficient conditions for a sequence to be a sub-moment sequence are established. A deep connection between the sub-moment measures and the moment measures is derived and the determinacy of the moment and sub-moment problems are related. This problem is further related to completion of positive Hankel matrices.
Aryal Saroj
Jafari Farhad
Putinar Mihai
No associations
LandOfFree
Sparse Moment Sequences does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Sparse Moment Sequences, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sparse Moment Sequences will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-639012