caa a22 4500 467932018 CHVBK 20180406152946.0 cr unu---uuuuu 170328e20061001xx s 000 0 eng 10.1007/s00020-005-1415-z doi (NATIONALLICENCE)springer-10.1007/s00020-005-1415-z The Spectral Carathéodory-Fejér Problem [Elektronische Daten] [H. Huang, S. Marcantognini, N. Young] 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 $${\mathbb{G}_{k}}$$ , 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 $${\mathbb{G}_{k}}$$ , which is solved completely in the case k=2. Birkhäuser Verlag, Basel, 2006 Spectral Carathéodory-Fejér interpolation nationallicence Schur functions nationallicence spectral Nevanlinna-Pick interpolation theory nationallicence symmetrized polydisc nationallicence Kobayashi metric nationallicence Huang H. Department of Mathematics, Tunghai University, 40704, Taichung, Taiwan aut Marcantognini S. Department of Mathematics, Instituto Venezolano de Investigaciones Científicas, P.O. Box 21827, 1020A, Caracas, Venezuela aut Young N. School of Mathematics and Statistics, University of Newcastle upon Tyne, NE1 7RU, England aut Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhäuser.ch 56/2(2006-10-01), 229-256 0378-620X 56:2<229 2006 56 20 https://doi.org/10.1007/s00020-005-1415-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-005-1415-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Huang H. Department of Mathematics, Tunghai University, 40704, Taichung, Taiwan aut NATIONALLICENCE 700 1- Marcantognini S. Department of Mathematics, Instituto Venezolano de Investigaciones Científicas, P.O. Box 21827, 1020A, Caracas, Venezuela aut NATIONALLICENCE 700 1- Young N. School of Mathematics and Statistics, University of Newcastle upon Tyne, NE1 7RU, England aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhäuser.ch 56/2(2006-10-01), 229-256 0378-620X 56:2<229 2006 56 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer