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
R. Pitts, Nevanlinna–Pick interpolation for non-commutative analytic Toeplitz algebras, Integral Equations Operator Theory 31 (1998), no. 3, 321– 337.  H. Dym, J contractive matrix functions, reproducing kernel spaces and interpolation, CBMS Lecture Notes, vol. 71, Amer. Math. , Rhodes Island, 1989.  G. Julia, Extension nouvelle d’un lemme de Schwarz, Acta Math. 42 (1920), 349–355.  V. Katsnelson, A. Kheifets, and P. Yuditskii. An abstract interpolation problem and the extension theory of isometric operators.
The choice T = 0 leads to the function S(z) = Σ11 (z). This function is analytic at β1 and β2 and it is readily seen that Σ11 (β2 ) = Σ11 ((0, 1)) = −1. Σ11 (β1 ) = Σ11 ((1, 0)) = 1 and Furthermore, 3r+4 1 − 11−4r 1 − |Σ11 (rβ1 )|2 lim = lim r→1 r→1 1 − r2 1 − r2 and 4−7r 1 − 11−8r 1 − |Σ11 (rβ2 )|2 = lim lim 2 r→1 r→1 1−r 1 − r2 Another choice of T = √ 2 11 7 0 √ 5 7 2 =1 2 = 5. 4) to S(z) = (1 − z1 )(1 − z2 ) 5 + 5z1 z2 − 2z12 − 3z1 − 5z2 3z1 − 7z2 + 4 + · . z1 z2 −4z1 −8z2 +11 z1 z2 −4z1 −8z2 +11 5z1 z2 − 9z1 − 5z2 + 2z12 + 7 A simple computation shows that S(rβ1 ) = 2r + 3 , 7 − 2r S(rβ2 ) = 3 − 5r .
1) and 1 − |S(rβ1 )|2 4 = ≤ 1, 2 r→1 1−r 5 lim 1 − |S(rβ2 )|2 = 5. r→1 1 − r2 lim References  M. Abate, Angular derivatives in strongly pseudoconvex domains, Proc. Sympos. , 52 (1991), 23–40.  J. Agler and J. E. McCarthy, Complete Nevanlinna-Pick kernels, J. Funct. , 175 (2000), 111–124.  N. G. Kre˘ın, Some questions in the theory of moments, Article II, Translations of Mathematical Monographs, Amer. Math. , 1962.  D. Alpay, V. Bolotnikov and T. Kaptano˘ glu, The Schur algorithm and reproducing kernel Hilbert spaces in the ball, Linear Algebra Appl.
A Bitangential Interpolation Problem on the Closed Unit Ball for Multipliers of the Arveson Space by Ball J.A., Bolotnikov V.