Linear perturbations of the Wigner distribution and the Cohen's class

Autor:	Cordero, Elena, Trapasso, S. Ivan
Rok vydání:	2018
Předmět:	Mathematics - Functional Analysis Mathematics - Classical Analysis and ODEs 42A38 42B35 46F10 46F12 81S30
Zdroj:	Anal. Appl. 18 (2020), no. 3, 385-422
Druh dokumentu:	Working Paper
DOI:	10.1142/S0219530519500052
Popis:	The Wigner distribution is a milestone of Time-frequency Analysis. In order to cope with its drawbacks while preserving the desirable features that made it so popular, several kind of modifications have been proposed. This contributions fits into this perspective. We introduce a family of phase-space representations of Wigner type associated with invertible matrices and explore their general properties. As main result, we provide a characterization for the Cohen's class. This feature suggests to interpret this family of representations as linear perturbations of the Wigner distribution. We show which of its properties survive under linear perturbations and which ones are truly distinctive of its central role. Comment: 37 pages, 1 figure. To appear in Analysis and Applications
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1811.07795 Zobrazit plný text záznamu View this record from Arxiv