A simple proof of the result that the Wigner transformation is of finite order. (English) Zbl 0692.46071
Summary: Using a set of functions with linear span that is dense in \(L^ 2({\mathbb{R}}^{2N})\) a simple proof is constructed of the result [discovered and proved by J. C. Varilly and J. M. Gracia- Bondia recently [J. Math. Phys. 28, 2390 (1987)] that the Wigner transformation is of order 24 and that its sixth power is the inverse Fourier transform (or Fourier cotransform).
MSC:
| 46N99 | Miscellaneous applications of functional analysis |
| 42B10 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
References:
| [1] | DOI: 10.1063/1.527776 · doi:10.1063/1.527776 |
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