منابع مشابه
On some results of entire functions of two complex variables using their relative lower order
Some basic properties relating to relative lower order of entire functions of two complex variables are discussed in this paper.
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whenever the right-hand side of (1.2) represents an analytic function in a neighborhood of the origin. When φ(x) is an entire function, the operator φ(D) has been studied by several authors (see, for example, [5, §11], [19, Chapter IX], [22] and [32]). The conjecture of Pólya and Wiman, proved in [8], [9] and [17], states that if f(x) ∈ L-P∗, then Df(x) is in the Laguerre-Pólya class for all su...
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We prove that if f is a real entire function of infinite order, then ff ′′ has infinitely many non-real zeros. In conjunction with the result of Sheil-Small for functions of finite order this implies that if f is a real entire function such that ff ′′ has only real zeros, then f is in the Laguerre-Pólya class, the closure of the set of real polynomials with real zeros. This result completes a l...
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In this paper, we study some growth properties of entire functions represented by a vector valued Dirichlet series on the basis of generalized relative Ritt order and generalized relative Ritt lower order.
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In this paper, we introduce the idea of relative order and type of entire functions represented by Banach valued Dirichlet series of two complex variables to generalize some earlier results. Proving some preliminary theorems on the relative order, we obtain sum and product theorems and we show that the relative order of an entire function represented by Dirichlet series is the same as that of i...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1956
ISSN: 0040-8735
DOI: 10.2748/tmj/1178244979