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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1999-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171299224453 |
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| 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. |
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| ISSN: | 0161-1712 1687-0425 |