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Products of Toeplitz operators on the Bergman space. (English) Zbl 1109.47023
The authors consider the Toeplitz operators on the Bergman space over the unit disc with the so-called quasihomogeneous symbols, i.e., with symbols of the form \(f(z)=e^{ip\theta}\varphi (r)\), where \(z=re^{i\theta}\) and \(p\) is an integer. They give necessary and sufficient conditions for the product of two Toeplitz operators to be a Toeplitz operator and an explicit formula for the symbol of such a product in certain cases.

MSC:
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
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