ISSN:
1531-5851
Keywords:
42B99
;
47B35
;
15A54
;
60G35
;
Positive extensions
;
Toeplitz operators
;
matrix functions on bitorus
;
Wiener algebra
;
band method
;
entropy
;
almost periodic functions
;
ARMA processes
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Let S be a band in Z2 bordered by two parallel lines that are of equal distance to the origin. Given a positive definite ℓ1 sequence of matrices {cj}j∈S we prove that there is a positive definite matrix function f in the Wiener algebra on the bitorus such that the Fourier coefficients $$\widehat{f(k)}$$ equal ck for k ∈ S. A parameterization is obtained for the set of all positive extensions f of {cj}j∈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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01274187
