Commuting Quasihomogeneous Toeplitz Operators on the Harmonic Bergman Space |
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Authors: | Xing-Tang Dong Ze-Hua Zhou |
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Institution: | 1. Department of Mathematics, Tianjin University, Tianjin, 300072, People’s Republic of China
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Abstract: | In this paper, we obtain a symmetry number for the commutator of quasihomogeneous Toeplitz operators on the harmonic Bergman space. Then we use it to characterize the commuting Toeplitz operators with quasihomogeneous symbols. Also, we show that a Toeplitz operator with an analytic or co-analytic monomial symbol commutes with another Toeplitz operator only in the trivial case. |
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