k^{th} order Slant Hankel Operators on the Polydisk

TL;DR

This paper introduces the concept of k^{th} order slant Hankel operators on the polydisk, providing conditions for their boundedness and exploring their algebraic properties.

Contribution

It defines k^{th} order slant Hankel operators on L^2(T^n) and characterizes their boundedness, commutativity, compactness, hyponormality, and isometric properties.

Findings

Necessary and sufficient conditions for boundedness

Characterization of algebraic properties of these operators

Extension of Hankel operator theory to higher orders

Abstract

In this paper, we initiate the notion of k^{th} order slant Hankel operators on L^2(T^n) for k greater than or equal to 2 and n greater than or equal to 1 where T^n denotes the n-torus. We give the necessary and sufficient condition for a bounded operator on L^2(T^n) to be a k^{th} order slant Hankel and discuss their commutative, compactness, hyponormal and isometric property.