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The Weyl calculus for hermitian matrices

Author(s): Brian Jefferies
Journal: Proc. Amer. Math. Soc. 124 (1996), 121-128.
MSC (1991): Primary 47A60, 47B15; Secondary 35E05, 15A60
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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:

[A]: R.F.V. Anderson, The Weyl functional calculus, J. Funct. Anal. 4 (1969), 240--267. MR 58:30405
[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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