Mellin Transform, Monomial Symbols, and Commuting Toeplitz Operators
Mellin Transform, Monomial Symbols, and Commuting Toeplitz Operators
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DOI：
10.1006/jfan.1997.3204
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发表时间：
1998-04
影响因子：
1.7
通讯作者：
Z. C̆uc̆ković;N. V. Rao
中科院分区：
文献类型：
--
作者：
Z. C̆uc̆ković;N. V. Rao
本文给出了Bergman空间上一个符号产生一个Toeplitz算子的充要条件，该算子与另一个符号为单项式的Toeplitz算子交换。结果用符号的梅林变换表示。作为推论，我们证明了一个带有径向符号的Toeplitz算子只能与另一个带有径向符号的算子交换。
Abstract In this paper we give necessary and sufficient conditions for a symbol that produces a Toeplitz operator on the Bergman space that commutes with another such operator whose symbol is a monomial. The result is stated in terms of the Mellin transform of the symbol. As a corollary, we show that a Toeplitz operator with a radial symbol may only commute with another such operator with a radial symbol.