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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