Schatten–von Neumann norm inequalities for two-wavelet localization operators associated with β-Stockwell transforms

Abstract

In this article we define two-wavelet localization operators corresponding to an irreducible and square-integrable representation of a locally compact Hausdorff group on a Hilbert space. The group structure admitting an irreducible and square-integrable representation which is related to β-Stockwell transform, that we shall use in this article β ∈ R have been introduced in Boggiatto et al. [P. Boggiatto, C. Fernandez, and A. Galbis, A group representation related to the Stockwell transform, Indiana Univ. Math. J. 58(5) (2009), pp. 2277–2296]. The Schatten–von Neumann norm inequalities of these two-wavelet localization operators are established. The traces and the trace class norm inequalities of the trace class two-wavelet localization operators are given.

Keywords:

• square-integrable representation
• two-wavelet localization operator
• Schatten–von Neumann class
• Stockwell transform

AMS Subject Classifications::

• Primary 47B10
• 47G10
• Secondary 22D10
• 43A80