Time-frequency Analysis of Born-Jordan Pseudodifferential Operators
arXiv:1601.05303 · doi:10.1016/j.jfa.2016.10.004
Abstract
Born-Jordan operators are a class of pseudodifferential operators arising as a generalization of the quantization rule for polynomials on the phase space introduced by Born and Jordan in 1925. The weak definition of such operators involves the Born-Jordan distribution, first introduced by Cohen in 1966 as a member of the Cohen class. We perform a time-frequency analysis of the Cohen kernel of the Born -Jordan distribution, using modulation and Wiener amalgam spaces. We then provide sufficient and necessary conditions for Born-Jordan operators to be bounded on modulation spaces. We use modulation spaces as appropriate symbols classes.
21 pages, 1 figure
References in corpus (2)
Cited by in corpus (4)
- Linear perturbations of the Wigner distribution and the Cohen's class
- On the reduction of the interferences in the Born-Jordan distribution
- Linear perturbations of the Wigner transform and the Weyl quantization
- Boundedness of Pseudodifferential Operators with symbols in Wiener amalgam spaces on Modulation Spaces