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The spectral Carathéodory-Fejér problem

Lookup NU author(s): Dr Huang Huang, Professor Stefania Marcantognini, Emeritus Professor Nicholas Young

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Abstract

The problem of the title is to construct an analytic k × k matrix-valued 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 script G signk, 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 script G signk, which is solved completely in the case k = 2. © 2006 Birkhäuser Verlag, Basel.

Publication metadata

Author(s): Huang H-N, Marcantognini SAM, Young NJ

Publication type: Article

Publication status: Published

Journal: Integral Equations and Operator Theory

Year: 2006

Volume: 56

Issue: 2

Pages: 229-256

ISSN (print): 0378-620X

ISSN (electronic): 1420-8989

Publisher: Birkhaeuser Verlag AG

URL: http://dx.doi.org/10.1007/s00020-005-1415-z

DOI: 10.1007/s00020-005-1415-z

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