Noncommutative complex analysis and Bargmann-Segal multipliers
Operator Algebras
2007-05-23 v1 Complex Variables
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.
Cite
@article{arxiv.math/9908025,
title = {Noncommutative complex analysis and Bargmann-Segal multipliers},
author = {Richard Rochberg and Nik Weaver},
journal= {arXiv preprint arXiv:math/9908025},
year = {2007}
}
Comments
10 pages