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A Jensen Inequality for a Family of Analytic Functions

Alex Brudnyi
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Abstract

We improve an estimate (obtained in "A.Brudnyi, Small amplitude limit cycles and the distribution of zeros of families of analytic functions, Ann. of Math. 154 (2) (2001), 227-243") for the average number of limit cycles of a planar polynomial vector field situated in a neighbourhood of the origin provided that the field in a larger neighbourhood is close enough to a linear center. The result follows from a new distributional inequality for the number of zeros of a family of univariate holomorphic functions depending holomorphically on a parameter.

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Alex Brudnyi. 2001-11-30. A Jensen Inequality for a Family of Analytic Functions. https://arxiv.org/abs/math/0112002

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