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The Weyl calculus for hermitian matrices


Author: Brian Jefferies
Journal: Proc. Amer. Math. Soc. 124 (1996), 121-128
MSC (1991): Primary 47A60, 47B15; Secondary 35E05, 15A60
DOI: https://doi.org/10.1090/S0002-9939-96-03143-7
MathSciNet review: 1301032
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Abstract: The Weyl calculus is a means of constructing functions of a system of hermitian operators which do not necessarily commute with each other. This note gives a new proof of a formula, due to E. Nelson, for the Weyl calculus associated with a system of hermitian matrices.


References [Enhancements On Off] (What's this?)

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  • [N] E. Nelson, Operants: A functional calculus for non-commuting operators, Functional Analysis and Related Fields, Proceedings of a conference in honour of Professor Marshal Stone (Univ. of Chicago, May 1968) (F.E. Browder, ed.), Springer-Verlag, Berlin, Heidelberg, and New York, 1970, pp. (172--187). MR 54:978
  • [R] W. Rudin, Real and complex analysis, 2nd ed., McGraw-Hill, New York, 1987. MR 88k:00002
  • [T] M.E. Taylor, Functions of several self-adjoint operators, Proc. Amer. Math. Soc. 19 (1968), 91--98. MR 36:3149

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Additional Information

Brian Jefferies
Affiliation: address School of Mathematics, University of New South Wales, New South Wales 2052, Australia
Email: B.Jefferies@unsw.edu.au

DOI: https://doi.org/10.1090/S0002-9939-96-03143-7
Keywords: Functional calculus, Weyl calculus, hermitian matrix, distribution
Received by editor(s): July 5, 1994
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society

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