Journal article
The Carathéodory–Toeplitz problem with partial data
Linear algebra and its applications, v 342(1), 149
15 Feb 2002
Abstract
We treat a positive extension problem in an algebra of periodic doubly infinite operator matrices. The given data have a stalactite-type pattern. The problem may be viewed as an operator-valued Carathéodory–Toeplitz problem with partially described data. Necessary and sufficient conditions are given for the existence of a solution, the set of all solutions is described and a maximum entropy result is obtained as well. In the matrix-valued case the problem was also considered by Alpay et al. [Linear Algebra Appl. 268 (1998) 247], where the problem was rephrased as an interpolation problem requiring symmetries and solutions were given in these terms. We shall also interpret our results in the context of cyclostationary stochastic processes.
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Details
- Title
- The Carathéodory–Toeplitz problem with partial data
- Creators
- Hugo J. Woerdeman - William & Mary
- Publication Details
- Linear algebra and its applications, v 342(1), 149
- Publisher
- Elsevier
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000173129100011
- Scopus ID
- 2-s2.0-31244431915
- Other Identifier
- 991021866365404721
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- Web of Science research areas
- Mathematics
- Mathematics, Applied