A comparison theorem for spaces of entire functions
نویسندگان
چکیده
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 کاملA Landing Theorem for Dynamic Rays of Subhyperbolic Entire Functions
Let f be a subhyperbolic entire transcendental function of finite order and let z0 be a repelling periodic point of f . We show that there exists at least one dynamic ray (injective curve to ∞ consisting of escaping points) that lands at z0. In fact, our result holds more generally, namely for any subhyperbolic entire function f for which each periodic address is realised by some dynamic ray in...
متن کاملCertain Hilbert Spaces of Entire Functions
1. Introduction. The research reported on in the present note was motivated by the following Proposition (F), due to Ernest Fischer ([5], see also [4] for an earlier version; actually Fischer proved a more general result, but the special case suffices as a point of departure for our discussion) : (F) Let P denote a homogeneous polynomial in si, • • • , z k with complex coefficients. Then every ...
متن کاملNecessary and Sufficient Conditions for Carlson's Theorem on Entire Functions.
A star on a Y (or a IT) wl'' be used throughout this paper to indicate that the index of the sum (or the product) is restricted to lie in A. Theorem 1 is an optimal extension of a celebrated theorem of Carlson which states that the only entire function/(z) satisfying (1.1) and (1.2) and such that/(ra) =0 for each positive integer ra is the null function f(z) =0. The necessity of condition (1.4)...
متن کاملVector ultrametric spaces and a fixed point theorem for correspondences
In this paper, vector ultrametric spaces are introduced and a fixed point theorem is given for correspondences. Our main result generalizes a known theorem in ordinary ultrametric spaces.
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: 1963
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1963-0147651-7