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Proceedings of the American Mathematical Society

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

 
 

 

A minimal decay rate for solutions of stable $n$th order homogeneous differential equations with constant coefficients


Author: David W. Kammler
Journal: Proc. Amer. Math. Soc. 48 (1975), 145-151
MSC: Primary 34C10
DOI: https://doi.org/10.1090/S0002-9939-1975-0369810-9
MathSciNet review: 0369810
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Abstract: In this paper we establish the existence of an envelope function (depending only on $n$ and $\alpha > 0$) which provides a pointwise bound on the size of any normalized solution $y$ of any homogeneous $n$th order differential equation with constant coefficients for which the roots of the corresponding characteristic polynomial have real parts which do not exceed $- \alpha$. An explicit representation for this envelope is obtained in the special case where these roots are further constrained to be real valued.


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Keywords: Minimal decay rate for exponential sums, Chebyshev polynomial on <!– MATH $[0, + \infty )$ –> <IMG WIDTH="73" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$[0, + \infty )$"> with exponential weight
Article copyright: © Copyright 1975 American Mathematical Society