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- W1980582014 abstract "States in classical mechanics are probability measures, and their Fourier transforms are continuous functions of positive type. States in the phase-space formulation of quantum mechanics are Wigner distribution functions, and their (symplectic) Fourier transforms have been characterized by Kastler [Commun. Math. Phys. 1, 14 (1965)] and Loupias and Miracle-Sole [Commun. Math. Phys. 2, 31 (1966); Ann. Insto. H. Poincaré 6, 39 (1967)] as being continuous functions of ‘‘ℏ-positive type.’’ In this paper, (Schwartz) distributions of ℏ-positive type, are defined and studied. It is shown that if such distributions are bounded on a certain sequence of test functions, then they are symplectic Fourier transforms of Wigner distribution functions. These results, are applied to a variety of problems ranging from ones involving the quantum Liouville equation to a problem in signal analysis." @default.
- W1980582014 created "2016-06-24" @default.
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- W1980582014 date "1989-11-01" @default.
- W1980582014 modified "2023-09-23" @default.
- W1980582014 title "Distributions of ℏ-positive type and applications" @default.
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- W1980582014 doi "https://doi.org/10.1063/1.528537" @default.
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