On kth-Order Slant Weighted Toeplitz Operator

Abstract EN

Let β={βn}n∈ℤ be a sequence of positive numbers with β0=1, 0<βn/βn+1≤1 when n≥0 and 0<βn/βn-1≤1 when n≤0.

A kth-order slant weighted Toeplitz operator on L2(β) is given by Uϕ=WkMϕ, where Mϕ is the multiplication on L2(β) and Wk is an operator on L2(β) given by Wkenk(z)=(βn/βnk)en(z), {en(z)=zk/βk}k∈ℤ being the orthonormal basis for L2(β).

In this paper, we define a kth-order slant weighted Toeplitz matrix and characterise Uϕ in terms of this matrix.

We further prove some properties of Uϕ using this characterisation.