On kth-order slant weighted Toeplitz operator

Let β = [formula: see text] be a sequence of positive numbers with β0 = 1, 0 < β(n)/β(n+1) ≤ 1 when n ≥ 0 and 0 < β(n)/β(n-1) ≤ 1 when n ≤ 0. A kth-order slant weighted Toeplitz operator on L(2)(β) is given by U(φ) = W(k)M(φ), where M(φ) is the multiplication on L(2)(β) and W(k) is an operator on L(2)(β) given by W(k)e(nk)(z) = (β(n)/β(nk))e(n)(z), [formula: see text] being the orthonormal basis for L(2)(β). In this paper, we define a kth-order slant weighted Toeplitz matrix and characterise U(φ) in terms of this matrix. We further prove some properties of U(φ) using this characterisation.