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Noncommutative complex analysis and Bargmann-Segal multipliers

Richard Rochberg·Nik Weaver
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Abstract

We state several equivalent noncommutative versions of the Cauchy-Riemann equations and characterize the unbounded operators on L^2(R) which satisfy them. These operators arise from the creation operator via a functional calculus involving a class of entire functions, identified by Newman and Shapiro [D. J. Newman and H. S. Shapiro, Fischer spaces of entire functions, in Entire Functions and Related Parts of Analysis (J. Koorevaar, ed.), AMS Proc. Symp. Pure Math. XI (1968), 360-369], which act as unbounded multiplication operators on Bargmann-Segal space.

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Richard Rochberg, Nik Weaver. 1999-08-06. Noncommutative complex analysis and Bargmann-Segal multipliers. https://arxiv.org/abs/math/9908025

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