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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Taylor-Dirichlet series and algebraic differential-difference equations

Author: Frank Wadleigh
Journal: Proc. Amer. Math. Soc. 80 (1980), 83-89
MSC: Primary 30B50
MathSciNet review: 574513
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Abstract: It is proved that if a convergent Taylor-Dirichlet series

$\displaystyle \sum\limits_{k = 0}^\infty {{P_k}(s){e^{ - {\lambda _k}s}},\quad ... ...{C}},{P_k}} (s) \in {\mathbf{C}}[s],\mathcal{R}({\lambda _k}) \uparrow \infty ,$

satisfies an algebraic differential-difference equation then the set of its exponents $ \{ {\lambda _k}\} _{k = 0}^\infty $ has a finite, linear, integral basis. This generalizes a theorem of A. Ostrowski.

An application of the theorem to a problem of oscillation in neuro-muscular systems is indicated.

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Additional Information

PII: S 0002-9939(1980)0574513-3
Article copyright: © Copyright 1980 American Mathematical Society

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