The spectral Carathéodory-Fejér problem
نویسنده
چکیده
The problem of the title is to construct an analytic k × k matrixvalued function in the unit disc with a number of prescribed derivatives at 0 and with spectral radius bounded by 1. We show that the problem can be reduced to an interpolation problem for the symmetrized polydisc Gk, and thereby show that, in the case of derivatives of orders 0 and 1 being prescribed, the problem is equivalent to the infinitesimal Kobayashi extremal problem for Gk, which is solved completely in the case k = 2. Mathematics Subject Classification (2000). Primary 30E05, 47A56; Secondary ?????
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