Some differential and integral equations with applications to Toeplitz operators
We solve a certain differential equation and system of integral equations. As applications, we characterize holomorphic symbols of commuting Toeplitz operators on the pluriharmonic Bergman space. In addition, pluriharmonic symbols of normal Toeplitz operators are characterized. Also, zero semi-commutators for certain classes of Toeplitz operators are characterized.
1991 Mathematics Subject ClassificationPrimary 32A10 45F05 Secondary 47B35
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