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

Marcel Berland

International Journal of Mathematics and Mathematical Sciences, 1999, vol. 22, 1-14

Abstract:

We introduce the notions of Ritt order and type to functions defined by the series ∑ n = 1 ∞ f n ( σ + i τ 0 ) exp ( − s λ n ) , s = σ + i τ , ( σ , τ ) ∈ R × R ( * ) indexed by τ 0 on R , where ( λ n ) 1 ∞ is a D -sequence and ( f n ) 1 ∞ is a sequence of entire functions of bounded index with at most a finite number of zeros. By definition, the series are B E -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.

Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:201753

DOI: 10.1155/S0161171299224453

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