On kth-Order Slant Weighted Toeplitz Operator. (17th July 2013) - Arora, S. C.; Kathuria, Ritu
Abstract : Let β = β n n ∈ ℤ be a sequence of positive numbers with β 0 = 1, 0 < β n / β n + 1 ≤ 1 when n ≥ 0 and 0 < β n / β n - 1 ≤ 1 when n ≤ 0 . A k th-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 n k ( z ) = (β n / β n k ) e n ( z ), e n ( z ) = z k / β k k ∈ ℤ being the orthonormal basis for L 2 ( β ) . In this paper, we define a k th-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.