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A Bitangential Interpolation Problem on the Closed Unit Ball by Ball J.A., Bolotnikov V.

By Ball J.A., Bolotnikov V.

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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. V. Gusev and A. Lindquist, From finite covariance windows to modeling filters: a convex optimization approach, SIAM Review 43(4) (2001), 645-675. ¨ [21] C. Carath´eodory, Uber die Winkelderivierten von beschr¨ ankten analytischen Funktionen, Sitzungber.

The space H(kd , E, E∗ ) can (and will) be identified with the tensor product Hilbert space H(kd ) ⊗ L(E, E∗ ). For multiindicies n = (n1 , . . , nd ) ∈ Nd we shall use the standard notations n1 + n2 + . . n2 ! . nd ! , z1n1 z2n2 . . zdnd = z n . Vol. 8]) that in the metric of H(kd ),   n! if n=m z n , z m H(kd ) = |n|! 6)   n! ∗ Fn Fn ∈ L(E) .  |n|! The next step is to introduce the operator–valued sesquilinear form n! ∗ [X, Y ]H(kd ) = Y Xn , |n|! 7) n∈N which makes sense and is L(E1 , E2 )-valued for every choice of Yn z n ∈ H(kd , E1 , E) Y (z) = Xn z n ∈ H(kd , E2 , E).

R→1 1 − r2 lim References [1] M. Abate, Angular derivatives in strongly pseudoconvex domains, Proc. Sympos. , 52 (1991), 23–40. [2] J. Agler and J. E. McCarthy, Complete Nevanlinna-Pick kernels, J. Funct. , 175 (2000), 111–124. [3] N. 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.

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