Weyl transforms and the products of two wavelet multiplier operators on locally compact abelian topological groups

Abstract

Let \(\alpha \) be a topological automorphism on a locally compact abelian group G, satisfies \(\alpha (p^{2})=p\) for all \(p\in G\). This paper deals with defining Fourier–Wigner, Wigner and Weyl transforms with respect to \(\alpha \), and among other things, it shows that Weyl transform has the same effect as Hilbert–Schmidt operators and the product of two wavelet multipliers.