By Ball J.A., Bolotnikov V.
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Extra info for A Bitangential Interpolation Problem on the Closed Unit Ball for Multipliers of the Arveson Space
3. 4) =1 on Bd , such that d d zj w ¯ Φj (z, w) − j, =1 Φjj (z, w) = D(z)D(w)∗ − B(z)B(w)∗ . 4. 3). 5. 5) and kernels Λ1 , . . , Λd subject to d (zj − w ¯j )Λj (z, w) = C(z)B(w)∗ − A(z)D(w)∗ , j=1 such that the kernel P(z, w) = Λ(z, w) Λ1 (z, w)∗ .. Λd (z, w)∗ Λ1 (z, w) Φ11 (z, w) .. ··· ··· Λd (z, w) Φ1d (z, w) .. 2)). 2. 1), let H(kd ) be the corresponding reproducing kernel Hilbert space. In this section we apply the preceding analysis to the operator-valued H(kd )-functions. To be more precise, let E and E∗ be two Hilbert spaces and let H(kd , E, E∗ ) denote the space of L(E, E∗ )-valued functions F (z) such that the function z → F (z)x, y E∗ belongs to H(kd )(= H(kd , C, C)) for every choice of x ∈ E and y ∈ E∗ .
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