Trigonometric Convexity for the Multidimensional Indicator after Ivanov
Aleksandr Mkrtchyan, Armen Vagharshakyan
TL;DR
This paper extends the concept of indicator functions to multiple complex variables, establishing a trigonometric convexity property and demonstrating the sharpness of the estimate using multidimensional Fourier analysis.
Contribution
It introduces a multidimensional analogue of trigonometric convexity for the indicator after Ivanov, a significant generalization from the one-variable case.
Findings
Proves a multidimensional trigonometric convexity inequality.
Shows the estimate is sharp in the multidimensional setting.
Utilizes multidimensional sectorial Fourier inversion in the proof.
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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Taxonomy
TopicsAnalytic and geometric function theory · Approximation Theory and Sequence Spaces · Differential Equations and Boundary Problems