Dual exponential polynomials and a problem of Ozawa
Dual exponential polynomials and a problem of Ozawa
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DOI：
10.1017/prm.2021.29
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发表时间：
2021-01
期刊：
影响因子：
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通讯作者：
J. Heittokangas;K. Ishizaki;K. Tohge;Z. Wen
中科院分区：
文献类型：
--
作者：
J. Heittokangas;K. Ishizaki;K. Tohge;Z. Wen
研究了整系数复线性微分方程组，其中一个系数是指数多项式，并且控制了所有其他系数的增长。如果这样的方程有指数多项式解$f$，则$f$的阶数和占优系数的阶数相等，并且这两个函数具有一定的对偶性质。本文的结果改进了一些作者的早期结果，并伴随着两个未解决的问题。
Complex linear differential equations with entire coefficients are studied in the situation where one of the coefficients is an exponential polynomial and dominates the growth of all the other coefficients. If such an equation has an exponential polynomial solution $f$, then the order of $f$ and of the dominant coefficient are equal, and the two functions possess a certain duality property. The results presented in this paper improve earlier results by some of the present authors, and the paper adjoins with two open problems.