On the order and lower order of entire functions with radially distributed zeros
نویسندگان
چکیده
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.
متن کاملOn the Number of Zeros of Successive Derivatives of Entire Functions of Finite Order
1 We use this occasion to point out that the condition lim inf log M (r) < 1 r-+c g(r) in Theorem 2 of [1] can be replaced by the somewhat weaker condition : there exists a, sequence r1, + oo such that log M (r,,) < g(r1,). It is clear from the proof that only this is actually used . Thus the following assertion is true THEOREM B. Let g(r) denote an arbitrary increasing function, defined in 0 <...
متن کاملDifferential Operators of Infinite Order and the Distribution of Zeros of Entire Functions
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...
متن کاملOn the lower order (R) of an entire Dirichlet series
© Annales de l’institut Fourier, 1974, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier...
متن کاملRelative order and type of entire functions represented by Banach valued Dirichlet series in two variables
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1983
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1983-0684637-0