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

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13). 10) if and only if S is subject to S(σ(ξ))∗ h(ξ) = g(ξ). 13). 15) Vol. 46 (2003) Bitangential Interpolation 157 that is, to S0 (σ(ξ))∗ S1 (σ(ξ))∗ h(ξ) = g(ξ). 13). 6 in terms of a Redheffer transform. 2, the transfer function of this transformation is not a Schur function anymore, but nevertheless, it has some special properties. 9. 17) and the parameter T from the class Sd (E ⊕ ∆∗ , E∗ ⊕ (⊕d1 E) ⊕ ∆) for some auxiliary Hilbert spaces ∆ and ∆∗ . Moreover, E∗ Θ11 (z) ∈ Bd (E, ) Θ21 (z) E ⊕ ∆∗ E∗ Θ12 (z) ∈ Sd (E∗ ⊕ (⊕d1 E) ⊕ ∆, ).

Potapov, S even Papers Translated from the Russian, Amer. Math. Soc. Transl. , 1988. ¨ [34] R. Nevanlinna, Uber beschr¨ ankte Funktionen, Ann. Acad. Sci. Fenn. Ser. A 32 (1939), no. 7. 164 Ball and Bolotnikov IEOT [35] M. Rosenblum and J. Rovnyak, Hardy classes and operator theory, Oxford University Press, 1985. [36] W. Rudin, F unction theory in the unit ball of Cn , Springer-Verlag, New York, 1980. [37] D. Sarason, Sub-Hardy Hilbert Spaces in the Unit Disk, University of Arkansas Lecture Notes in the Matehmatical Sciences, Wiley, 1994.

Ball, Interpolation problems of Pick-Nevanlinna and Loewner type for meromorphic matrix functions, Integral Equations and Operator Theory, 6 (1983), 804-840. [12] J. A. Ball and V. , to appear. A. Ball, I. Gohberg and L. Rodman, Interpolation of Rational Matrix Functions, Birkh¨ auser Verlag, Basel, 1990. A. Ball, I. Gohberg and L. Rodman, Boundary Nevanlinna-Pick interpolation for rational matrix functions, J. Math. Systems, Estimation, and Control 1 (1991), 131164. A. W. Helton, Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix-functions: parametriztion of the set of all solutions, Integral Equations and Operator Theory 9 (1986), 155-203.

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