Special orthonormal basis for $L^2$ functions on the unit circle
Bull. Korean Math. Soc. 2017 Vol. 54, No. 6, 2013-2027
Published online 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
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