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Title: Extremal problems for matrix-valued polynomials on the unit circle and applications to multivariate stationary sequences
Authors: Klotz, L ×
Lasarow, Andreas #
Issue Date: Nov-2003
Publisher: Academic press inc elsevier science
Series Title: Journal of approximation theory vol:125 issue:1 pages:42-62
Abstract: The paper is devoted to a matrix generalization of a problem studied by Grenander and Rosenblatt (Trans. Amer. Math. Soc. 76 (1954) 112-126) and deals with the computation of the infimum Delta of integral(T) Q*(z)M(dz)Q(z), where M is a non-negative Hermitian matrix-valued Borel measure on the unit circle T and Q runs through the set of matrix-valued polynomials with prescribed values of some of their derivatives at a finite set J of complex numbers. Under some additional assumptions on M and J, the value of A is computed and the results are applied to linear prediction problems of multivariate weakly stationary random sequences. A related truncated problem is studied and further extremal problems are briefly discussed. (C) 2003 Elsevier Inc. All rights reserved.
URI: 
ISSN: 0021-9045
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Non-KU Leuven Association publications
× corresponding author
# (joint) last author

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