A rich structure related to the construction of analytic matrix functions

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• 作者：D.C. Brown^a ; ^{d.c.brown@newcastle.ac.uk} ; Z.A. Lykova^a ; ^{Zinaida.Lykova@ncl.ac.uk} ; N.J. Young^b ; ^a ; ^{N.J.Young@leeds.ac.uk}
• 关键词：90C22 ; 30E05 ; 93D21 ; 93B50 ; 47N10 ; 47N70
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：272
• 期：4
• 页码：1704-1754
• 全文大小：644 K
• 卷排序：272

文摘

We study certain interpolation problems for analytic 2×22×2 matrix-valued functions on the unit disc. We obtain a new solvability criterion for one such problem, a special case of the μ  -synthesis problem from robust control theory. For certain domains XX in C2C2 and C3C3 we describe a rich structure of interconnections between four objects: the set of analytic functions from the disc into XX, the 2×22×2 matricial Schur class, the Schur class of the bidisc, and the set of pairs of positive kernels on the bidisc subject to a boundedness condition. This rich structure combines with the classical realisation formula and Hilbert space models in the sense of Agler to give an effective method for the construction of the required interpolating functions.