Journal article
Positive matrix functions on the bitorus with prescribed Fourier coefficients in a band
The Journal of fourier analysis and applications, v 5(1), 21
01 Jan 1999
Abstract
Let S be a band in Z(2) bordered by two parallel lines that are of equal distance to the origin. Given a positive definite l(1) sequence of matrices {c(j)} (j is an element of S), we prove that there is a positive definite matrix function f in the Wiener algebra on the bitorus such that the Fourier coefficients <(f(k))over cap> equal c(k) for k is an element of S. A parameterization is obtained for the set of all positive extensions f of {c(j)} (j is an element of S). We also prove that among all matrix functions with these properties, there exists a distinguished one that maximizes the entropy. A formula is given for this distinguished matrix function. The results are interpreted in the context of spectral estimation of ARMA processes.
Metrics
Details
- Title
- Positive matrix functions on the bitorus with prescribed Fourier coefficients in a band
- Creators
- M Bakonyi - Georgia State UniversityL Rodman - William & MaryI M Spitkovsky - William & MaryH J Woerdeman - William & Mary
- Publication Details
- The Journal of fourier analysis and applications, v 5(1), 21
- Publisher
- Springer Nature
- Number of pages
- 24
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000079464600003
- Scopus ID
- 2-s2.0-0345884544
- Other Identifier
- 991021866357404721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied