@inproceedings{e3e1bb8e65cf4103a803df73380e7e47,
title = "Taylor domination, difference equations, and Bautin ideals",
abstract = "We compare three approaches to studying the behavior of an analytic function f (z) = [formula presented] from its Taylor coefficients. The first is “Taylor domination” property for f (z) in the complex disk DR, which is an inequality of the form [formula presented]. The second approach is based on a possibility to generate ak via recurrence relations. Specifically, we consider linear non-stationary recurrences of the form [formula presented], …, with uniformly bounded coefficients. In the third approachweassume that ak = ak(λ) are polynomials in a finite-dimensional parameter λ ∈ ℂn.We study “Bautin ideals” Ik generated by a1(λ), …, ak(λ) in the ring ℂ [λ] of polynomials in λ. These three approaches turn out to be closely related. We present some results and questions in this direction.",
keywords = "Bautin ideals, Domination of initial Taylor coefficients, Recurrence relations",
author = "Dmitry Batenkov and Yosef Yomdin",
note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2016.; 18th International Conference on Difference Equations and Applications, ICDEA 2012 ; Conference date: 23-07-2012 Through 27-07-2012",
year = "2016",
doi = "10.1007/978-3-662-52927-0_21",
language = "الإنجليزيّة",
isbn = "9783662529263",
series = "Springer Proceedings in Mathematics and Statistics",
pages = "303--319",
editor = "Cushing, {Jim M.} and Pinto, {Alberto A.} and Saber Elaydi and {i Soler}, {Lluis Alseda}",
booktitle = "Difference Equations, Discrete Dynamical Systems and Applications - ICDEA 2012",
}