Krein's sufficient condition for indeterminacy states that a positive measure on the real line, having moments of all orders, is indeterminate provided it has density with respect to Lebesgue measure and that this density has a finite logarithmic integral. We generalize this result and we also give
On M. G. Krein's contribution to the moment problem
✍ Scribed by A. A. Nudel'man
- Book ID
- 112471286
- Publisher
- Springer
- Year
- 1995
- Tongue
- English
- Weight
- 965 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0041-5995
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📜 SIMILAR VOLUMES
## Abstract An indefinite trigonometric moment problem is solved using the one‐step completion and the geometry involved in extending factorizations in Kreîn spaces. In addition, a description of all the solutions is obtained as well as a simple characterization of the case when there exists exactl
In one of his works, M.G. Krein discovered an analogy between polynomials orthogonal on the unit circle and generalized eigenfunctions of certain differential systems. We used some ideas of this paper to obtain new results in spectral analysis of Sturm-Liouville operators.
## Abstract The article is devoted to the solution of the infinite‐dimensional variant of the complex moment problem, and to the uniqueness of the solution. The main approach is illustrated for the best explanation on the one‐dimensional case. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)