Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30B50

Retrieve articles in all journals with MSC: 30B50


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0574513-3
PII: S 0002-9939(1980)0574513-3
Article copyright: © Copyright 1980 American Mathematical Society