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A non-commutative F&M Riesz Theorem
Michael T. Jury, Robert T. W. Martin, Edward J. Timko
We extend results on analytic complex measures on the complex unit circle to a non-commutative multivariate setting. Identifying continuous linear functionals on a certain self-adj…
Non-commutative measure theory: Henkin and analytic functionals on -algebras
Raphaël Clouâtre, Edward J. Timko
Henkin functionals on non-commutative -algebras have recently emerged as a pivotal link between operator theory and complex function theory in several variables. Our…
Analytic functionals for the non-commutative disc algebra
Raphaël Clouâtre, Robert T. W. Martin, Edward J. Timko
The main objects of study in this paper are those functionals that are analytic in the sense that they annihilate the non-commutative disc algebra. In the classical univariate case…
Gelfand transforms and boundary representations of complete Nevanlinna--Pick quotients
Raphaël Clouâtre, Edward J. Timko
The main objects under study are quotients of multiplier algebras of certain complete Nevanlinna--Pick spaces, examples of which include the Drury--Arveson space on the ball and th…