Linear differential equations with entire coefficients of small growth |
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| Authors: | J K Langley |
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| Institution: | (1) School of Mathematical Sciences, King Abdulaziz University, University of Nottingham, Nottingham, NG72RD, UK;(2) Department of Mathematics, Faculty of Education, P.O. Box 15758, Jeddah, 21454, Saudi Arabia |
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| Abstract: | We prove that if
n \geqq 3 n \geqq 3 and A0, ?, An-2 A_0, \ldots, A_{n-2} are entire functions of small growth, not all polynomials, then the linear differential equation¶¶ w(n) + ?j=0n-2 Aj w(j) = 0 w^{(n)} + \sum\limits_{j=0}^{n-2} A_j w^{(j)} = 0 ¶¶ cannot have a fundamental set of solutions each with few zeros. |
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