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By Ball J.A., Bolotnikov V.

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Extra resources for A Bitangential Interpolation Problem on the Closed Unit Ball for Multipliers of the Arveson Space

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1997), pages 89-138, OT 122, Birkhauser-Verlag, Basel-Boston-Berlin, 2001. [17] V. , to appear. Vol. 46 (2003) Bitangential Interpolation 163 [18] 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. [19] 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.

24) and that −1 (I − T Σ22 ) T Σ21 (I − ZΣ111 )−1 ZΣ112 (I − T Θ22 ) −1 = (I − T Θ22 ) − (I − T Σ22 ) −1 −1 . 16). 20) of Σ that the function Σ21 (z) is a Schur function. 21) belongs to Bd (E, ). 22) can be considered as the Vol. 46 (2003) Bitangential Interpolation 159 Redheffer transform of the Schur function Z(z). 20). 7. Appendix: a numerical example In conclusion we illustrate the general construction done in Sections 4 and 5 by a simple numerical example. 1) r→1 and 1 − |S(rβ1 )|2 1 − |S(rβ1 )|2 ≤ 1, lim ≤ 5.

G. Kre˘ın, Some questions in the theory of moments, Article II, Translations of Mathematical Monographs, Amer. Math. , 1962. [4] D. Alpay, V. Bolotnikov and T. Kaptano˘ glu, The Schur algorithm and reproducing kernel Hilbert spaces in the ball, Linear Algebra Appl. 342 (2002), 163–186. [5] D. Alpay and C. , to appear. [6] A. Arias and G. Popescu, Noncommutative interpolation and Poisson transforms, Israel J. Math. 115 (2000), 205–234. [7] N. Aronszajn, Theory of reproducing kernels, Trans. Amer.

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A Bitangential Interpolation Problem on the Closed Unit Ball for Multipliers of the Arveson Space by Ball J.A., Bolotnikov V.


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