On the Compactness of Higher Order slant Hankel and slant Toeplitz Operators

Abstract

Here, we study $k^{\text{th}}$ order slant Hankel and $k^{\text{th}}$ order slant Toeplitz operators on Hardy spaces. Contrary to the behavior of the classical Toeplitz operators, the symbol of the compression of a $k^{\text{th}}$ order slant Toeplitz operator cannot be determined uniquely by the operator. Likewise, the symbol of the compression of a $k^{\text{th}}$ order slant Hankel operator is also not unique. The nature of the boundedness of these operators has also been studied to compare their spectral properties and compactness criteria.