In this paper we study reproducing kernel Hilbert and Banach spaces of pairs. These are a generalization of reproducing kernel Krein spaces and, roughly speaking, consist of pairs of Hilbert (or Banach) spaces of functions in duality with respect to a sesquilinear form and admitting a left and right reproducing kernel. We first investigate some properties of these spaces of pairs. It is then proved that to every function K(z, ω) analytic in z and ω* there is a neighborhood of the origin that can be associated with a reproducing kernel Hilbert space of pairs with left reproducing kernel K(z, ω) and right reproducing kernel K(ω, z)*.
D. Alpay. A theorem on reproducing kernel Hilbert spaces of pairs. Rocky Mountain J. Math. 22 (1992), no. 4, 1243-1258.
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