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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On solutions of linear differential equations with real zeros; proof of a conjecture of Hellerstein and Rossi
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by Franz Brüggemann PDF
Proc. Amer. Math. Soc. 113 (1991), 371-379 Request permission

Abstract:

We prove the following conjecture that is due to Hellerstein and Rossi: Let $\left \{ {{w_1}, \ldots ,{w_n}} \right \}$ be a fundamental system of \[ Lw = {w^{(n)}} + {a_{n - 1}}(z){w^{(n - 1)}} + \cdots + {a_0}(z)w \equiv 0\] with polynomials ${a_j}(z)(0 \leq j \leq n - 1)$. If each ${w_k}(1 \leq k \leq n)$ has only finitely many nonreal zeros, then there exists a polynomial $q(z)$ such that ${u_k}: = \exp (q(z)){w_k}(1 \leq k \leq n)$ form a fundamental system of a homogeneous linear differential equation with constant coefficients.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 113 (1991), 371-379
  • MSC: Primary 34A20; Secondary 30D35, 34C10
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1057941-9
  • MathSciNet review: 1057941