On integrals over a convex set of the Wigner distribution

2019/01/22 by Delourme, Bérangère, Duyckaerts, Thomas, Lerner, Nicolas · 1 citation
#34L05 #94A12 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1901.07262

Abstract

We provide an example of a normalized L²(\mathbb R) function u such that its Wigner distribution \mathcal W(u,u) has an integral >1 on the square [0,a]×[0,a] for a suitable choice of a. This provides a negative answer to a question raised by P. Flandrin in 1988. Our arguments are based upon the study of the Weyl quantization of the indicatrix of \mathbb R₊×\mathbb R₊ along with a precise numerical analysis of its discretization.

Cited by

• Spectral asymptotics of pseudodifferential operators with discontinuous symbols

Related

• Integrating the Wigner Distribution on subsets of the phase space, a Survey
• Regularity of distributions of Wigner integrals
• Zeros of the Wigner Distribution and the Short-Time Fourier Transform
• The wave front set of the Wigner distribution and instantaneous frequency
• Sp(2,ℤ) invariant Wigner function on even dimensional vector space