Outer factorization of operator valued weight functions on the torus

• Autorzy: Ray Cheng
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

outer factorization   Toeplitz operator   prediction theory   Szegö's infimum   multivariate stationary process  

Kategorie tematyczne

• 47A68: Factorization theory (including Wiener-Hopf and spectral factorizations)
• 60G20: Generalized stochastic processes

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994
• Tom: 110
• Numer: 1
• Strony: 19-34

Daty

wydano

1994

otrzymano

1993-03-16

poprawiono

1993-09-03

Twórcy

autor

Ray Cheng

• Department of Mathematics, University of Louisville, Louisville, Kentucky 40292, U.S.A.

Bibliografia

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