Noncommutative complex analysis and Bargmann-Segal multipliers

Rochberg, Richard; Weaver, Nik

doi:10.1090/S0002-9939-01-05897-X

Noncommutative complex analysis and Bargmann-Segal multipliers
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by Richard Rochberg and Nik Weaver PDF

Proc. Amer. Math. Soc. 129 (2001), 2679-2687 Request permission

Abstract:

We state several equivalent noncommutative versions of the Cauchy-Riemann equations and characterize the unbounded operators on $L^{2}(\mathbf {R})$ 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, which act as unbounded multiplication operators on Bargmann-Segal space.

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