Matrices of Toeplitz operators on Hardy spaces over bounded domains
Bull. Korean Math. Soc. 2017 Vol. 54, No. 4, 1421-1441
Published online July 31, 2017
Young-Bok Chung
Chonnam National University
Abstract : We compute explicitly the matrix represented by the Toeplitz operator on the Hardy space over a smoothly finitely connected bounded domain in the plane with respect to special orthonormal bases consisting of the classical kernel functions for the space of square integrable functions and for the Hardy space. The Fourier coefficients of the symbol of the Toeplitz operator are obtained from zeroth row vectors and zeroth column vectors of the matrix. And we also find some condition for the product of two Toeplitz operators to be a Toeplitz operator in terms of matrices.
Keywords : Toeplitz operator, Toeplitz matrices, Laurent operator, Hardy space, Ahlfors map, Szego kernel
MSC numbers : Primary 47B35, 30C40
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