منابع مشابه
A Theorem on Entire Functions
Let G(k) = ∫ 1 0 g(x)e kxdx, g ∈ L1(0, 1). The main result of this paper is the following theorem. THEOREM 1. There exists g 6≡ 0, g ∈ C∞ 0 (0, 1), such that G(kj) = 0, kj < kj+1, limj→∞ kj =∞, limk→∞ |G(k)| does not exist, lim supk→+∞ |G(k)| = ∞. This g oscillates infinitely often in any interval [1− δ, 1], however small δ > 0 is. MSC: 30D15, 42A38, 42A63
متن کاملGrowth analysis of entire functions of two complex variables
In this paper, we introduce the idea of generalized relative order (respectively generalized relative lower order) of entire functions of two complex variables. Hence, we study some growth properties of entire functions of two complex variables on the basis of the definition of generalized relative order and generalized relative lower order of entire functions of two complex variables.
متن کاملOn Newton’s Method for Entire Functions
The Newton map Nf of an entire function f turns the roots of f into attracting fixed points. Let U be the immediate attracting basin for such a fixed point of Nf . We study the behavior of Nf in a component V of C \ U . If V can be surrounded by an invariant curve within U and satisfies the condition that for all z ∈ Ĉ, N f ({z}) ∩ V is a finite set, we show that V contains another immediate ba...
متن کاملPrime Entire Functions
Factorizations of various functions are discussed. Complete factorizations of certain classes of functions are given. In particular it is shown that there exist primes of arbitrary growth.
متن کاملDynamics of Entire Functions
Complex dynamics of iterated entire holomorphic functions is an active and exciting area of research. This manuscript collects known background in this field and describes several of the most active research areas within the dynamics of entire functions. Complex dynamics, in the sense of holomorphic iteration theory, has been a most active research area for the last three decades. A number 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: Kodai Mathematical Journal
سال: 1977
ISSN: 0386-5991
DOI: 10.2996/kmj/1138847516