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Schwarz-Pick inequalities for the Schur-Agler class on the polydisk and unit ball. (English) Zbl 1157.30019
The notion of a realization has an important role in many areas of operator theory, linear systems theory, and interpolation theory. The authors use the notion of a unitary realization to derive estimates of derivatives of functions on the polydisk and unit ball. Some open problems are also discussed.
MSC:
30C80Maximum principle; Schwarz’s lemma, Lindelöf principle, etc. (one complex variable)
32A30Generalizations of function theory to several variables
47B32Operators in reproducing-kernel Hilbert spaces
47A48Operator colligations, vessels, linear systems, characteristic functions, etc.
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