On kth-Order Slant Weighted Toeplitz Operator. (17th July 2013)

• Record Type: Journal Article
• Authors: Arora, S. C.; Kathuria, Ritu
• Other Names: Agouzal A. Academic Editor.; Ibeas A. Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2013(2013)
• Publication Date: 2013-07-17
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2013/960853
• Languages: English
• ISSNs: 2356-6140

Abstract

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.