Algebras of distributions suitable for phase‐space quantum mechanics. I

The twisted product of functions on R2N is extended to a *‐algebra of tempered distributions that 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...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical physics 1988-04, Vol.29 (4), p.869-879
Main Authors: GRACIA-BONDIA, J. M, VARILLY, J. C
Format: Article
Language:English
Subjects:
Classical and quantum physics: mechanics and fields
Exact sciences and technology
Physics
Quantum mechanics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The twisted product of functions on R2N is extended to a *‐algebra of tempered distributions that 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.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.528200