Analogue of slant Hankel operators on the Lebesgue space of n-torus

Abstract

In this paper, the multivariate analogue of slant Hankel operator on $L^2(\mathbb {T}^n)$, ($n\ge 1$, a natural number), the Lebesgue space of square integrable functions defined on $\mathbb {T}^n$, where $\mathbb {T}$ is the unit circle, is introduced. Various characterizations are obtained for a bounded operator on $L^2(\mathbb {T}^n)$  to be a kth- order slant Hankel operator  ($k\ge 2$, a fixed integer).