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The multiplicative Weyl functional calculus. (English) Zbl 0239.47010


MSC:

47A60 Functional calculus for linear operators
47B25 Linear symmetric and selfadjoint operators (unbounded)
22E25 Nilpotent and solvable Lie groups
35J10 Schrödinger operator, Schrödinger equation
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References:

[1] Anderson, R. F.V, The Weyl functional calculus, J. Functional Analysis, 4, 240-267 (1969) · Zbl 0191.13403
[2] Anderson, R. F.V, On the Weyl functional calculus, J. Functional Analysis, 6, 110-115 (1970) · Zbl 0196.14302
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[4] Loupias, G.; Miracle-Sole, S., \(C^∗\)-Algèbres des systèmes canoniques, I, Comm. Math. Phys., 2, 31-48 (1966) · Zbl 0144.23401
[5] Loupias, G.; Miracle-Sole, S., \(C^∗\)-Algèbres des systèmes canoniques, II, Ann. I.H.P., Sect. A, 6, 39-58 (1967) · Zbl 0168.23505
[6] Moyal, J. E., Quantum mechanics as a statistical theory, (Proc. Cambridge Phil. Soc., 45 (1949)), 99-124 · Zbl 0031.33601
[7] Pool, J. C.T, Mathematical aspects of the Weyl correspondence, J. Math. Phys., 7, 66-76 (1966) · Zbl 0139.45903
[8] Segal, I. E., Transforms for operators and symplectic automorphisms over a locally compact abelian group, Math. Scand., 13, 31-43 (1963) · Zbl 0208.39002
[9] Trotter, H., Approximation of semigroups of operators, Pacific J. Math., 8, 887-919 (1958) · Zbl 0099.10302
[10] Wigner, E., On the quantum correction for thermodynamic equilibrium, Phys. Rev., 40, 749-759 (1932)
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