|
Noncommutative complex analysis and Bargmann-Segal multipliers
Author(s):
Richard
Rochberg;
Nik
Weaver
Journal:
Proc. Amer. Math. Soc.
129
(2001),
2679-2687.
MSC (2000):
Primary 46L89, 47B32;
Secondary 30D15
Posted:
February 9, 2001
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
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.
References:
-
- [1]
- J. Aniansson, Some Integral Representations in Real and Complex Analysis, Doctoral Thesis, Royal Institute of Technology, Stockholm (1999).
- [2]
- S. T. Ali, J.-P. Antoine, J.-P. Gazeau, and U. A. Mueller, Coherent states and their generalizations: a mathematical overview, Rev. Math. Phys. 7 (1995), 1013-1104. MR 97b:81040
- [3]
- C. A. Berger and L. A. Coburn, Toeplitz operators on the Segal-Bargmann space, Trans. Amer. Math. Soc. 301 (1987), 813-829. MR 88c:47044
- [4]
- R. Boas, Entire Functions, Academic Press (1954). MR 16:914f
- [5]
- A. A. Borichev, The polynomial approximation property in Fock-type spaces, Math. Scand. 82 (1998), 256-264. CMP 99:01
- [6]
- D. Cichon and J. Stochel, On Toeplitz operators in Segal-Bargmann spaces, Univ. Iagel. Acta Math. 34 (1997), 35-43. MR 98d:47061
- [7]
- A. Connes, Noncommutative geometry, Academic Press (1995). MR 95j:46063
- [8]
- E. G. Effros, Advances in quantized functional analysis, Proc. ICM (Berkeley, California, 1986), 906-916, AMS (1987). MR 89e:46064
- [9]
- G. B. Folland, Harmonic Analysis in Phase Space, Princeton (1989). MR 92k:22017
- [10]
- J. Janas, Unbounded Toeplitz operators in the Bargmann-Segal space, Studia Math. 99 (1991), 87-99. MR 92j:47046
- [11]
- J. Janas and J. Stochel, Unbounded Toeplitz operators in the Segal-Bargmann space, II, J. Funct. Anal. 126 (1994), 418-447. MR 95m:47040
- [12]
- J. E. Moyal, Quantum mechanics as a statistical theory, Proc. Cambridge Philos. Soc. 45 (1949), 99-124. MR 10:582d
- [13]
- J. von Neumann, Die eindeutigkeit der Schrödingerschen operatoren, Math. Ann. 104 (1931), 570-578.
- [14]
- 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. MR 38:2333
- [15]
- -A Hilbert space of entire functions related to the operational calculus, manuscript.
- [16]
- M. A. Rieffel, Non-commutative tori -- a case study of non-commutative differentiable manifolds, Contemp. Math. 105 (1990), 191-211. MR 91d:58012
- [17]
- K. Seip and R. Wallstén, Density theorems for sampling and interpolation in the Bargmann-Fock space. II, J. Reine Angew. Math. 429 (1992), 107-113. MR 93g:46026b
- [18]
- S. L. Woronowicz, Differential calculus on compact matrix pseudogroups (quantum groups), Comm. Math. Phys. 122 (1989), 125-170. MR 90g:58010
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
46L89, 47B32,
30D15
Retrieve articles in all Journals with MSC
(2000):
46L89, 47B32,
30D15
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:
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
Posted:
February 9, 2001
Communicated by:
David R. Larson
Copyright of article:
Copyright
2001,
American Mathematical Society
|
Comments: webmaster@ams.org