Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

De Gruyter eBooks

5 The Weyl transform

Maurice A. de Gosson

Published Jun 21, 2021• 0 citations
Publisher
DOI
10.1515/9783110722772-005

Related papers

The Weyl Transform

Springer eBooks•Mar 31, 2006•1 citation

Weyl Transforms

Wong, M W

Springer eBooks•Jan 1, 1998•6 citations

Compact Weyl Transforms

Springer eBooks•Mar 31, 2006•0 citations

The conditional Weyl transform and its generalization

Leon W. Cohen, Patrick J. Loughlin

Journal of Pseudo-Differential Operators and Applications•Dec 20, 2012•0 citations

Wigner Transforms and Weyl Transforms

Man Wah Wong

The Fourier–Wigner transform of two functions is first defined and is given an alternative expression. The Wigner transform is then defined to be the Fourier transform of the Fourier–Wigner transform. The Moyal identity, which is an analog of the Plancherel formula, is then proved for the Wigner transform. The Weyl transform with a given symbol is then defined in terms of the Wigner transform. Another formula for the Weyl transform with a given symbol is then proved and used to establish the fact that the product of two Weyl transforms is also a Weyl transform with symbol given by a twisted convolution of the two given symbols.

Chapman & Hall/CRC eBooks•Jun 28, 2022•0 citations

The Weyl correspondence in the linear canonical transform domain

Amit Kumar, Akhilesh Prasad, Pankaj Jain

The main objective of the paper is to generalize and enrich the Weyl transform by introducing the Weyl correspondence in the linear canonical transform (LCT) domain. In this paper, we propose the linear canonical-Wigner transform in harmonic analysis of phase space along with the admissible Wigner-Ville distribution (WVD) and Weyl transform in the LCT domain and discuss some useful results. Further we establish the relationship between the Wigner-Ville distribution and the Weyl transform in the LCT domain.

Filomat•Jan 1, 2023•3 citations
The Fourier–Wigner transform of two functions is first defined and is given an alternative expression. The Wigner transform is then defined to be the Fourier transform of the Fourier–Wigner transform. The Moyal identity, which is an analog of the Plancherel formula, is then proved for the Wigner transform. The Weyl transform with a given symbol is then defined in terms of the Wigner transform. Another formula for the Weyl transform with a given symbol is then proved and used to establish the fact that the product of two Weyl transforms is also a Weyl transform with symbol given by a twisted convolution of the two given symbols.
The main objective of the paper is to generalize and enrich the Weyl transform by introducing the Weyl correspondence in the linear canonical transform (LCT) domain. In this paper, we propose the linear canonical-Wigner transform in harmonic analysis of phase space along with the admissible Wigner-Ville distribution (WVD) and Weyl transform in the LCT domain and discuss some useful results. Further we establish the relationship between the Wigner-Ville distribution and the Weyl transform in the LCT domain.