Analytic Range Functions of Several Variables

Cheng, R.

Canadian journal of mathematics, Tome 47 (1995) no. 3, pp. 462-473

Résumé

Let C be a separable Hilbert Space, and let Λ be the halfplane {(m, n) ∈ Ζ 2 : m ≥ 1} ∪ {(0, n) ∈ Ζ 2 : n ≥ 0} of the integer lattice. Consider the subspace Mc (Λ) of on the torus spanned by the C-valued trigonometric functions {Ceims+int : с ∈ C, (m, n) ∈ Λ}. The notion of a Λ-analytic operator on Mc (Λ) is defined with respect to the family of shift operators {Smn }Λ on MC (Λ) given by (Smnƒ)(eis , eit ) = eims+intƒ(eis , eit ). The corresponding concepts of inner function, outer function and analytic range function are explored. These ideas are applied to the spectral factorization problem in prediction theory.

Détail

DOI : 10.4153/CJM-1995-026-2

Mots-clés : 47A68, 60G25, operator valued function, inner function, outer function, analytic range function, spectral factorization

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