TY  - BOOK
AU  - Gosson,Maurice de
TI  - Wigner transform
T2  - Advanced textbooks in mathematics
SN  - 9781786343093 (pbk : alk. paper)
U1  - 530.1595 23
PY  - 2017///
CY  - New Jersey : 
PB  - World Scientific
KW  - Phase space (Statistical physics)
KW  - Statistical mechanics
N1  - Includes bibliographical references and index; 1. Phase space translations and reflections --
2. The cross-wigner transform --
3. The Cross-Ambiguity function --
4. Weyl operators --
5. Symplectic covariance --
6. The moyal identity --
7. The feichtinger algebra --
8. The cohen class --
9. Gaussians and Hermite functions --
10. Sub-Gaussian estimates --
11. Moyal star product and twisted convolution --
12. Probabilistic interpretation of the Wigner transform --
13. Mixed quantum states and the density operator --
14. The KLM coditions and the Narcowich-Wigner spectrum --
15. Wigner transform and quantum blobs --
Appendices
N2  - This book provides an in-depth and rigorous study of the Wigner transform and its variants. They are presented first within a context of a general mathematical framework, and then through applications to quantum mechanics. The Wigner transform was introduced by Eugene Wigner in 1932 as a probability quasi-distribution which allows expression of quantum mechanical expectation values in the same form as the averages of classical statistical mechanics. It is also used in signal processing as a transform in time-frequency analysis, closely related to the windowed Gabor transform
ER  -