By Ball J.A., Bolotnikov V.
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Additional resources for A Bitangential Interpolation Problem on the Closed Unit Ball for Multipliers of the Arveson Space
2, 244–266.  I. V. P. Potapov, S even Papers Translated from the Russian, Amer. Math. Soc. Transl. , 1988. ¨  R. Nevanlinna, Uber beschr¨ ankte Funktionen, Ann. Acad. Sci. Fenn. Ser. A 32 (1939), no. 7. 164 Ball and Bolotnikov IEOT  M. Rosenblum and J. Rovnyak, Hardy classes and operator theory, Oxford University Press, 1985.  W. Rudin, F unction theory in the unit ball of Cn , Springer-Verlag, New York, 1980.  D. Sarason, Sub-Hardy Hilbert Spaces in the Unit Disk, University of Arkansas Lecture Notes in the Matehmatical Sciences, Wiley, 1994.
11) 156 Ball and Bolotnikov IEOT 3. 12) for some Schur function S ∈ Sd (E, E∗ ⊕ (⊕d1 E)): S(z) = E∗ S0 (z) : E→ , S1 (z) ⊕d1 E Z(z) = z1 IE ... zd IE . 13) Proof: The equivalence (1 ⇔ 2) follows from a more general fact that F is a contractive multiplier between two reproducing kernel Hilbert spaces H(K1 ) and H(K2 ) of functions analytic on a set Ω if and only if the kernel K2 (z, w) − F (z)K1 (z, w)F (w)∗ is positive on Ω. To show that (2 ⇔ 3), we represent KF as KF (z, w) = IE − F (z)F (w)∗ + F (z)Z(z)Z(w)∗ F (w)∗ , 1 − z, w or, equivalently, as KF (z, w) = A(z)A(w)∗ − B(z)B(w)∗ , 1 − z, w where A(z) = IE F (z)Z(z) and B(z) = F (z).
To appear. Vol. 46 (2003) Bitangential Interpolation 163  V. Bolotnikov and H. Dym, On degenerate interpolation, entropy and extremal problems for matrix Schur functions, Integral Equations Operator Theory, 32 (1998), No. 4, 367–435.  V. Bolotnikov and H. Dym, On boundary interpolation for matrix Schur functions, Preprint MCS99-22, Department of Mathematics, The Weizmann Institute of Science, Israel. I. V. Gusev and A. Lindquist, From finite covariance windows to modeling filters: a convex optimization approach, SIAM Review 43(4) (2001), 645-675.