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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Noncommutative complex analysis and Bargmann-Segal multipliers


Authors: Richard Rochberg and Nik Weaver
Journal: Proc. Amer. Math. Soc. 129 (2001), 2679-2687
MSC (2000): Primary 46L89, 47B32; Secondary 30D15
Published electronically: February 9, 2001
MathSciNet review: 1838792
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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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Additional Information

Richard Rochberg
Affiliation: Department of Mathematics, Washington University, St. Louis, Missouri 63130
Email: rr@math.wustl.edu

Nik Weaver
Affiliation: Department of Mathematics, Washington University, St. Louis, Missouri 63130
Email: nweaver@math.wustl.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05897-X
PII: S 0002-9939(01)05897-X
Received by editor(s): September 27, 1999
Received by editor(s) in revised form: January 14, 2000
Published electronically: February 9, 2001
Communicated by: David R. Larson
Article copyright: © Copyright 2001 American Mathematical Society