On the Ritt order and type of a certain class of functions defined by BE-Dirichletian elements

We introduce the notions of Ritt order and type to functions defined by the series ∑n=1∞fn(σ+iτ0)exp(−sλn),      s=σ+iτ,(σ,τ)∈R×R                                            (*) indexed by τ0 on R, where (λn)1∞ is a D-sequence and (fn)1∞ is a sequence of entire functions of bounded index with at most...

Full description

Saved in:
Bibliographic Details
Main Author: Marcel Berland
Format: Article
Language:English
Published: Wiley 1999-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171299224453
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We introduce the notions of Ritt order and type to functions defined by the series ∑n=1∞fn(σ+iτ0)exp(−sλn),      s=σ+iτ,(σ,τ)∈R×R                                            (*) indexed by τ0 on R, where (λn)1∞ is a D-sequence and (fn)1∞ is a sequence of entire functions of bounded index with at most a finite number of zeros. By definition, the series are BE-Dirichletian elements. The notions of order and type of functions, defined by B-Dirichletian elements, are considered in [3, 4]. In this paper, using a technique similar to that used by M. Blambert and M. Berland [6], we prove the same properties of Ritt order and type for these functions.
ISSN:0161-1712
1687-0425