Geodesic
Outer factorization of operator valued weight functions on the torus
Studia Mathematica, Tome 110 (1994) no. 1, pp. 19-34

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

An exact criterion is derived for an operator valued weight function $W(e^{is},e^{it})$ on the torus to have a factorization $W(e^{is},e^{it}) = Φ(e^{is},e^{it})*Φ(e^{is},e^{it})$, where the operator valued Fourier coefficients of Φ vanish outside of the Helson-Lowdenslager halfplane $Λ = {(m,n) ∈ ℤ^2: m ≥ 1} ∪ {(0,n): n ≥ 0}$, and Φ is "outer" in a related sense. The criterion is expressed in terms of a regularity condition on the weighted space $L^2(W)$ of vector valued functions on the torus. A logarithmic integrability test is also provided. The factor Φ is explicitly constructed in terms of Toeplitz operators and other structures associated with W. The corresponding version of Szegö's infimum is given.
DOI : 10.4064/sm-110-1-19-34
Keywords: outer factorization, Toeplitz operator, prediction theory, Szegö's infimum, multivariate stationary process

Ray Cheng 1

1 
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Ray Cheng. Outer factorization of operator valued weight functions on the torus. Studia Mathematica, Tome 110 (1994) no. 1, pp. 19-34. doi: 10.4064/sm-110-1-19-34

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