Studies of linear difference equations
by
Katsuya Ishizaki
Department of Mathematics, Nippon Institute of Technology, 4-1 Gakuendai Miyashiro Minamisaitama Saitama 345-8501, Japan

(1)

n å j=0  aj(z)f(z+j)=0,

where a_j, j=0, ..., n (a_na₀ =/= 0) are polynomials.
We investigate the growth of entire solutions of (1) using a certain Wiman-Valiron type method, (see, for instance [1]). In connection with the growth properties of entire solutions, we also mention the questions posed by Ramis. [3].

References
[1] Hayman, W.K., The local growth of power series: A survey of the Wiman-Valiron method. Canad. Math. Bull. 17 (1974), 317-358.
[2] Ishizaki, K. and N. Yanagihara, Wiman-Valiron methods for difference equations, Preprint.
[3] Ramis, J.-P., About the growth of entire functions solutions of linear algebraic q-difference equations, Annales Fac. Sci. Toulouse, Ser. 6 I (1992), 53-94.

Date received: May 17, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahk-65.