Bicomplex Extensions of Slant Hankel Operators and Their Theoretic Properties

In this paper, we introduce and study a bicomplex analog of slant Hankel operators acting on the bicomplex Hilbert space L BC 2 ( U BC ) . Motivated by the classical theory of slant Hankel operators defined on L 2 ( T ) , we extend the underlying framework to the setting of bicomplex-valued functions. For a symbol φ = φ 1 e 1 + φ 2 e 2 in L BC ∞ , we define the associated slant bicomplex Hankel operator via its matrix representation with respect to the standard orthonormal basis, preserving the characteristic slant structure. We investigate fundamental operator-theoretic properties of these operators, including boundedness and norm estimates, and establish conditions for an operator to be a slant bicomplex Hankel operator. Utilizing the idempotent decomposition of bicomplex numbers, we derive representations that allow the reduction of certain problems to classical complex components.