The non-tangential boundary behavior of the matrix-valued rational inner functions on bounded symmetric domain

The non-tangential boundary behavior of the matrix-valued rational inner functions on bounded symmetric domain

Knese [Proc. LMS 111(2015), pp. 1261–1306] proved every rational inner function on polydisc has a non-tangential limit at every point of the Shilov boundary. We extended his result to the case of functions on general bounded symmetric domains. Namely, every rational inner function on a bounded symme...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2023-01, Vol.151 (4), p.1539-1551
Hauptverfasser: Wang, Kai, Zhang, Shuyi
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description Knese [Proc. LMS 111(2015), pp. 1261–1306] proved every rational inner function on polydisc has a non-tangential limit at every point of the Shilov boundary. We extended his result to the case of functions on general bounded symmetric domains. Namely, every rational inner function on a bounded symmetric domain has a non-tangential limit of modulus 1 at every point of the Shilov boundary. We also prove that every matrix-valued rational inner function on tube-type domain has a unitary non-tangential limit at every point of the Shilov boundary.
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title The non-tangential boundary behavior of the matrix-valued rational inner functions on bounded symmetric domain
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