Weyl transforms associated with a singular second-order differential operator

Cyrine Baccar and Lakhdar Tannech Rachdi

Vol. 219 (2005), No. 2, 201–220

DOI: 10.2140/pjm.2005.219.201

Abstract

For a class of singular second-order differential operators Δ, we define and study the Weyl transforms W_σ associated with Δ, where σ is a symbol in S^m, for m ∈ ℝ. We give criteria in terms of σ for boundedness and compactness of the transform W_σ.

Keywords

Weyl transform, compact operator, Fourier–Wigner transform

Mathematical Subject Classification 2000

Primary: 42A38, 65R10

Milestones

Received: 20 November 2003

Revised: 7 April 2004

Published: 1 April 2005