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

DOI:
https://doi.org/10.1090/S0002-9939-01-05897-X

Published electronically:
February 9, 2001

MathSciNet review:
1838792

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Abstract | References | Similar Articles | Additional Information

Abstract: We state several equivalent noncommutative versions of the Cauchy-Riemann equations and characterize the unbounded operators on 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:
https://doi.org/10.1090/S0002-9939-01-05897-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