On the Growth of Composite Entire Functions

ＯｎｔｈｅＧｒｏｗｔｈｏｆＣｏｍｐｏｓｉｔｅＥｎｔｉｒｅＦｕｎｃｔｉｏｎｓＱｉａｏＪｉａｎｙｏｎｇ（乔建永）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＦｕｄａｎＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ，２００４３３）Ａｂｓｔｒａｃｔ：Ｌｅｔｆａｎ...     

On the ℂ-differentiability of mappings of Banach spaces

We study the monogeneity conditions for -differentiable mappings of domains of a Banach space and establish criteria of -differentiability of a mapping at a point.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1336–1342, October, 1994.     

On Subharmonic Extensions

Recently V. Anandam has established the following theorem: Suppose that u(x) is a subharmonic function defined outside a compact setin R~n.Then for any sufficiently large r>0 there exist a nonconstant subharmonic function s(x) in R~n and a constant a≥0 such that for |x|>r     

On the Singular Direction of Entire Functions

In this paper, after defining a normal criterion with a parameter and a singular direction of an entire function corresponding to a normal criterion, we shall prove the following theorem.Theorem 1 Suppose that f(z) is a transcendental entire function. Then there exists a direction Δ: argz = θ0 (0≤0<2π) which is a singular direction of f(z) corresponding to every normal criterion with a parameter.From theorem 1 we deduce at once existence of some singular directions.     

On the Bounded Variation of Operator-Valued Functions

In[1],the Kothe nuclear sequence spaces are described and in[2]the characte-rization of the semi-nuclear and the barreled locally convex spaces by the boundedvariation of functions respectively.In this paper several kinds of bounded variationof operator-valued functions are studied. Let X and Y are Banach spaces,T(t):[0,1]→L(X,Y)be a operator-valued fun-ction.We called T(t)be uniformly bounded variation,if there exist a constantM>0,such that for any partition △:0=t_0相似文献   

On the closure of the sum of two uniform algebras on compact sets in ℂ

Necessary and sufficient conditions on a compact set X in ? and a self-homeomorphism ψ of the plane ? are studied under which any function continuous on X can be approximated uniformly on X by functions of the form p + h ° ψ, where p is a polynomial in a complex variable and h is a rational function whose poles belong to the bounded components of the complement to the compact set ψ(X).     

On the Complexity of the Julia Sets of Rational Functions

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On the Pseudo-Primeness of Meromorphic Functions of Infinite Order

In this paper the pseudo -primeness of meromorphic functions of infinite order is dissoussed in detail and quite a few result are obtained, which are improvments of that of Ozawa.     

On the Choquet Charge of δ-superharmonic Functions

Let u v be positive superharmonic functions in a general potential-theoretic setting, where these functions have a Choquet-type integral representation by minimal such functions with Choquet charges (i.e. representing measures) and , respectively. We show that on the contact set {u – v = 0} of the -superharmonic function u – v, if this set is properly interpreted as the set of those minimal superharmonic functions s which satisfy lim sup _{T s} v/u = 1 for the co-fine neighborhood filter T _s associated with s. In the setting of classical potential theory for Laplace's equation this result improves on results obtained by Fuglede in 1992.     

On the Irredundant Forms of Fuzzy Switching Functions

ＯｎｔｈｅＩｒｒｅｄｕｎｄａｎｔＦｏｒｍｓｏｆＦｕｚｚｙＳｗｉｔｃｈｉｎＦｕｎｃｔｉｏｎｓTXＯｎｔｈｅＩｒｒｅｄｕｎｄａｎｔＦｏｒｍｓｏｆＦｕｚｚｙＳｗｉｔｃｈｉｎｇＦｕｎｃｔｉｏｎｓＰｅｉＤａｏｗｕ（ＹａｎｃｈｅｎｇＴｅａｃｈｅｒｓＣｏｌｅｇｅ，...     

On the injectivity of twisted spherical means on ℂ n

In this paper we study the injectivity and injectivity sets for the twisted spherical means on ℂ ⁿ . These results are then used to study the same problems on the reduced Hiesenberg group.     

On the Rational Spline Functions

Since Schoenberg's fundamental paper was published in 1946, the theory of polynomial spline functions developed rapldly and was rich in contents. Spline functions have wide range of applications to numerical approximation.But to certain functions, for example, to the function with singular points, the interpolation by polynomial spline is not always efficient and reasonable. Since 1973 some authors have investigated the rational spline functions, and abtained a lot of results. But     

On the Compactness of the Hypercomplex Commutator in Hölder Continuous Functions Spaces

This paper is devoted to the compactness of the hypercomplex commutator S _γ M _a ? M _a S _γ, where S _γ is the Cauchy singular integral operator (in the Douglis sense), a is a Hölder continuous hypercomplex function and M _a is the multiplication operator given by M _a f = a f. We extend a known compactness sufficient condition for the commutator of the Cauchy singular integral operator to the frame of the hypercomplex analysis, where γ is merely required to be an arbitrary regular closed Jordan curve.     

On the Convergence of ω1 Sequences of Real Functions

We study sets of points at which ω₁ sequences of real functions from a given class F converge. As F we consider continuous functions, first class of Baire, Borel measurable functions, functions with Baire property and Lebesgue measurable functions. Connections of those problem with additional set-theoretic axioms are discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the Accurate Order of Approximatlon of Some Classes of Functions

1.Introduction. Let E_n(f)_([a,b])be the best approximation of degree n to f(x)∈C_([a,b]), w_k(f,δ)_([a,b]) is the k-th modulus of smoothness of f(x) in [a,b]. In 1914, S.Bernstein [1] proved that E_n(|x|)_([-1.1]) exists. Since then, S. Bernstein, S.Nikol'skii, M. Hasson and the author worked in this direction to     

On the Pseudo—Primensee of Meromorphic Functions of Infinite Order

In this paper the pseudo-primeness of meromorphic functions of infinite order is disscossed in detail and quite a few result are obtained,which ae improvments of that of Ozawa.