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Abstract: The classical Hardy spaces of analytic functions on the complex open unit disk have played an important role in the development of operator theory and function theory. Several-variable Hardy spaces (Drury-Arveson spaces) of analytic functions on the open unit ball in several complex dimensions are now providing similarly powerful tools for modern multi-variable operator theory.

We will present recent results extending the seminal concept of Aleksandrov-Clark measures for the Hardy-Schur class of contractive analytic functions on the disk, and the deBranges-Rovnyak model for completely non-coisometric contractions on Hilbert space from one to several (commuting and non-commuting) variables.

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Gexin Yu

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