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arXiv · 1503.04026

On global non-oscillation of linear ordinary differential equations with polynomial coefficients

Dmitry Novikov·Boris Shapiro
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Abstract

In this note we show that a linear ordinary differential equation with polynomial coefficients is globally non-oscillating in $\mathbb{C} P^1$ if and only if it is Fuchsian, and at every its singular point any two distinct characteristic exponents have distinct real parts. As a byproduct of our study, we obtain a new explicit upper bound for the number of zeros of exponential polynomials in a horizontal strip.

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Dmitry Novikov, Boris Shapiro. 2015-03-13. On global non-oscillation of linear ordinary differential equations with polynomial coefficients. https://arxiv.org/abs/1503.04026

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