Trigonometric Convexity for the Multidimensional Indicator after Ivanov
Abstract
Multidimensional indicator after Ivanov is a generalization of the notion of indicator, that is well-known for analytic functions in one complex variable, to analytic functions in several complex variables. We prove an analogue of trigonometric convexity for it. Additionally, we show that our estimate is sharp. The proof is based on the multidimensional analogue of the sectorial Fourier inversion formula.
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