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Analytic Range Functions of Several Variables
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- Journal:
- Canadian Journal of Mathematics / Volume 47 / Issue 3 / 01 June 1995
- Published online by Cambridge University Press:
- 20 November 2018, pp. 462-473
- Print publication:
- 01 June 1995
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- Article
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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.
on the torus spanned by the 