Algebras of distributions suitable for phase‐space quantum mechanics. I
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Gracia Bondía, José M.
Várilly Boyle, Joseph C.
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Abstract
The twisted product of functions on R^2N is extended to a *-algebra of
tempered distributions which contains the rapidly decreasing smooth
functions, the distributions of compact support, and all polynomials,
and moreover is invariant under the Fourier transformation. The
regularity properties of the twisted product are investigated. A
matrix presentation of the twisted product is given, with respect to
an appropriate orthonormal basis, which is used to construct a family
of Banach algebras under this product.
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Keywords
Quantum mechanics in phase space, Moyal product, Tempered distributions
Citation
https://aip.scitation.org/doi/10.1063/1.528200