- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 Special orthonormal basis for $L^2$ functions on the unit circle Bull. Korean Math. Soc. 2017 Vol. 54, No. 6, 2013-2027 https://doi.org/10.4134/BKMS.b160697Published online July 7, 2017Printed November 30, 2017 Young-Bok Chung Chonnam National University Abstract : We compute explicitly the matrices represented by Toeplitz operators on the Hardy space over the unit circle with respect to a special orthonormal basis constructed by author in terms of their symbols. And we also find a necessary condition for the matrix generated by the product of two Toeplitz operators with respect to the basis to be a Toeplitz matrix by a direct calculation and we finally solve commuting problems of two Toeplitz operators in terms of symbols. This is a generalization of the classical results obtained regarding to the orthonormal basis consisting of the monomials. Keywords : Toeplitz operator, Toeplitz matrices, Hardy space, Szego kernel MSC numbers : Primary 47B35, 30C40 Downloads: Full-text PDF