A Jensen Inequality for a Family of Analytic Functions

Details A Jensen Inequality for a Family of Analytic Functions A Jensen Inequality for a Family of Analytic Functions

2001-11-30

arxiv.org/abs/math/0112002v1

Mathematics

Complex Variables

Scientific paper

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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