On a Class of Fractal Interpolation Functions

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On Rubel’s Problem in the Class of Linear Operators on the Space of Analytic Functions

In this paper, we describe all derivation pairs of linear operators that act in spaces of functions analytic in domains.     

Oscillation of Functions in the Hölder Class

Potential Analysis - We study the size of the set of points where the α-divided difference of a function in the Hölder class Λα is bounded below by a fixed positive constant....     

A Discrete Limit Theorem for the Matsumoto Zeta‐Function in the Space of Analytic Functions

In the paper, a discrete distribution of the Matsumoto zetafunction is considered. It is proved that the probability measure , converges weakly as .     

Interpolation Methods for the Evaluation of 2π-Periodic Finite Baire Measure

We discuss the definition and effectiveness of a Padé-type approximation to 2π-periodic finite Baire measures on [-π,π]. In the first two sections we recall the definitions and basic properties of the Padré-type approximants to harmonic functions in the unit disk and to L ^p -functions on the unit circle. Section 3 deals with the extension of these definitions and properties to a finite 2π-periodic Baire measure. Finally, section 4 is devoted to a study of the convergence of a sequence of such approximants, in the weak star topology of measures.     

Interpolation Methods for the Evaluation of 2π-Periodic Finite Baire Measure

We discuss the definition and effectiveness of a Padé-type approximation to 2-periodic finite Baire measures on [-,]. In the first two sections we recall the definitions and basic properties of the Padré-type approximants to harmonic functions in the unit disk and to L ^p -functions on the unit circle. Section 3 deals with the extension of these definitions and properties to a finite 2-periodic Baire measure. Finally, section 4 is devoted to a study of the convergence of a sequence of such approximants, in the weak star topology of measures.     

On Singularities of Generating Functions of Pólya Frequency Sequences of Finite Order

Let E be a closed set in C satisfying the conditions: (i) E is symmetric with respect to the real axis, (ii) E {z:|z|1} = . For any r 1 there exists a function f(z) satisfying the properties: (i) f(z) is a generating function of a Pólya frequency sequence of order r, (ii) the singularity set of f(z) is E {1}.     

On the Convolution of a Finite Number of Analytic Functions Involving a Generalized Srivastava–Attiya Operator

The present paper gives several subordination results involving a generalized Srivastava–Attiya operator (defined below). Among the results presented in this paper include also a sufficiency condition for the convexity of the convolution of certain functions and a sharp result relating to the convolution structure. We also mention various useful special cases of the main results including those which are related to the Zeta function.     

A Class of Meromorphic Bazilevič-Type Functions Defined by a Differential Operator

Ukrainian Mathematical Journal - We introduce a new subclass of meromorphic Bazilevi?-type functions defined with the help of a differential operator. We study some interesting properties of...     

Second-Order Expansion for a Class of Quasidifferentiable Functions

Suppose f, g:R~n→R are quasidifferentiable, and for an interval〔x,y〕:R~none has 0∈〈g(s)+g(s),y-x〉,s∈(x,y). Then there exists an η∈(x,y) suchthat     

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.     

Domains of Holomorphy of Generating Functions of Pólya Frequency Sequences of Finite Order*

A domain is the domain of holomorphy of the generating function of a Pólya frequency sequence of order r if and only if it satisfies the following conditions: (A) G contains the point z = 0, (B) G is symmetric with respect to the real axis, (C) T = dist(0,G)G.     

P≠NP for the Reals with Various Analytic Functions

We show that non-deterministic machines in the sense of L. Blum, M. Shub, and S. Smale (1989, Bull. Amer. Math. Soc.21) defined over wide classes of real analytic structures are more powerful than the corresponding deterministic machines.     

On the Approximation of Continuous Functions by Pal-Type Interpolation Polynomials

Let us denote by -1=x_n相似文献   

A Remark on Subgroup Separability in the Class of Finite π-Groups

We prove that if a group G is residually , then for every -subgroup of the group G, the set of -roots from this subgroup is a -separable -subgroup.