Abstract
We show that the problem of studying the Bergman-Toeplitz operators with functional symbols on a plane domain is, in a certain sense, the problem of studying the pseudodifferential operators on a half-line.
The symbols of the pseudodifferential operators we obtain are slowly varying in the additive sense at +∞ and in the multiplicative sense at 0 in the variable x.With respect to the dual variable the operators are a mixture of additive Wiener-Hopf operators and multiplicative Mellin convolutions.
The essential spectra of operators from the Toeplitz operator algebra are in general massive (have positive plain Lebesgue measure).
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Rabinovich, V., Vasilevski, N. (2000). Bergman-Toeplitz and pseudodifferential operators. In: de Arellano, E.R., Vasilevski, N.L., Shapiro, M., Tovar, L.M. (eds) Complex Analysis and Related Topics. Operator Theory Advances and Applications, vol 114. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8698-7_15
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DOI: https://doi.org/10.1007/978-3-0348-8698-7_15
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