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Multidimensional indicator after Ivanov is a generalization of the notion ofindicator, that is well-known for analytic functions in one complex variable,to analytic functions in several complex variables. We prove an analogue oftrigonometric convexity for it. Additionally, we show that our estimate issharp. The proof is based on the multidimensional analogue of the sectorialFourier inversion formula.

Trigonometric Convexity for the Multidimensional Indicator after Ivanov