Given a bounded symmetric domain in , we consider the Clark measures , , associated with a rational inner function from into the unit disc in . We show that , where is the dimension of the Šilov boundary of and is a suitable constant. Denoting with the closure of the space of holomorphic polynomials in , we characterize the for which when is a polydisc; we also provide some necessary and some sufficient conditions for general domains
Clark measures associated with rational inner functions on bounded symmetric domains / M. Calzi. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 1088-6826. - 153:(2025), pp. 3043-3061. [Epub ahead of print] [10.1090/proc/17194]
Clark measures associated with rational inner functions on bounded symmetric domains
M. Calzi
2025
Abstract
Given a bounded symmetric domain in , we consider the Clark measures , , associated with a rational inner function from into the unit disc in . We show that , where is the dimension of the Šilov boundary of and is a suitable constant. Denoting with the closure of the space of holomorphic polynomials in , we characterize the for which when is a polydisc; we also provide some necessary and some sufficient conditions for general domains
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