Fourier coefficients of continuous functions

It is well known that the Fourier coefficients of continuous functions with respect to classical orthogonal systems (trigonometric, Haar, and Walsh) can be estimated via the moduli of continuity of the functions. However, not all orthonormal systems possess this property. We obtain necessary and sufficient conditions on orthonormal systems such that the Fourier coefficients of continuous functions with respect to these orthonormal systems can be estimated via the moduli of continuity in a certain sense.     

Weakly Equilibrium Cantor-type Sets

Cantor-type sets are constructed as the intersection of the level domains for simple sequences of polynomials. This allows to obtain Green functions with various moduli of continuity and compact sets with preassigned growth of Markov’s factors.     

广义拟容量的C-右连续性

本文探讨广义容量的性质,得到如下结果：（a）具有C-右连续,即关于紧集连续的凸拟容量是凸容量;（b）一大类广义容量具有C-右连续性;（c）凸拟容量的准上积分是凸Choquet容量．此外,给出具有C-右连续性的弱拟容量的可容性定理．本文还利用上述结果研究调和空间上正超调和函数的缩减函数和扫除函数．     

Continuity properties of fractional powers,of the logarithm,and of holomorphic semigroups

We establish the continuity of the functions mentioned in the title (viewed as functions mapping operators onto operators) with respect to the gap and related finer topologies. Improved versions of results of Hille/Phillips and Kato concerning perturbations of holomorphic semigroups are easy consequences of our results.     

多元推广的Bernstein算子的逼近性质

构造了一类一致收敛于被逼近函数的多元序列,以此序列为基础,运用多元函数的全连续模及部分连续模来刻画这种多元推广的Bernstein算子的逼近性质,不仅得出了理论逼近结果,而且给出了数值逼近的例子.     

Rational Interpolation for Stieltjes Functions

The continuity conclusions about rational Hermite interpolating functions are given under some conditions. On that basis, we establish the convergence results for the paradiagonal sequences of the rational interpolants for Stieltjes functions and Hamburger functions.     

Separately continuous mappings with values in inductive limits

Generalizations of the classical results of Dini and Osgood on sequences of continuous functions are obtained. Based on these generalizations, we establish a Bairetype theorem concerning the size of their point set of joint continuity of separably continuous mappings of products of Baire spaces and spaces with first countability axiom in certain inductive limits of increasing sequences of locally convex metrizable spaces containing, in particular, such well-known nonmetrizable spaces as the space of finitary sequences and space of Schwartz sampling functions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 3, pp. 380–384, March, 1992.     

First-order regularity of convex functions on Carnot Groups

We prove that h-convex functions on Carnot groups of step two are locally Lipschitz continuous with respect to any intrinsic metric. We show that an additional measurability condition implies the local Lipschitz continuity of h-convex functions on arbitrary Carnot groups. To the Memory of Q. G.     

Приближение функций многих переменных классов H p Ω полиномами по системе Хаара

In the paper, problems of approximation of functions indicated in the title are studied in the case when a majorant of their mixed modulus of continuity is given. Two forms of approximation (linear and nonlinear) are considered: the classical linear approximation by polynomials with respect to the Haar system when the indices lie in hyperbolic crosses; and the best M-term approximation by polynomials also with respect to the Haar system. For the corresponding quantities, exact estimates are obtained as to their order of magnitude.     

Preservation of persistence and stability under intersections and operations,part 1: Persistence

New results about convergence of sets and functions in possibly infinite-dimensional spaces are derived in a simple and unified way from two results dealing with the continuity with respect to a parameter of the intersection of two convex sets depending on this parameter.     

Subrecursive functions on partial sequences

The paper studies a domain theoretical notion of primitive recursion over partial sequences in the context of Scott domains. Based on a non-monotone coding of partial sequences, this notion supports a rich concept of parallelism in the sense of Plotkin. The complexity of these functions is analysed by a hierarchy of classes similar to the Grzegorczyk classes. The functions considered are characterised by a function algebra generated by continuity preserving operations starting from computable initial functions. Its layers are related to those above by showing , thus generalising results of Schwichtenberg/Müller and Niggl. Received: 18 November 1996     

Approximation by means of piecewise linear functions

In the present paper we use piecewise linear functions in order to obtain representations and estimates for the remainder in approximating continuous functions by positive linear operators. Applications of these results for Bernstein and Stancu’s operators are also presented. In addition, we give some partial results concerning the best constant problem for Bernstein operators with respect to the second order modulus of continuity.     

The enumeration of sequences with respect to structures on a bipartition

We give a method for enumerating sequences over a finite alphabet with respect to certain maximal configurations. The required generating functions are obtained as solutions of systems of linear equations. The method utilizes a combinatorial decomposition of sequences into maximal sub-configurations.     

On the properties of sequences of fuzzy-valued Choquet integrable functions

In this paper, we focus on investigating the properties of sequences of fuzzy-valued Choquet (for short, (C)-) integrable functions. Firstly, the concept of uniform (C)-integrabiliy and other new concepts like uniform absolute continuity and uniform boundedness for sequences of fuzzy-valued (C)-integrable functions are introduced and then the relations among them are discussed. As the applications of these concepts, we also present several convergence theorems for sequences of fuzzy-valued (C)-integrable functions by using uniform (C)-integrability.     

Continuity of Solutions of a Class of Fractional Equations

In practice many problems related to space/time fractional equations depend on fractional parameters. But these fractional parameters are not known a priori in modelling problems. Hence continuity of the solutions with respect to these parameters is important for modelling purposes. In this paper we will study the continuity of the solutions of a class of equations including the Abel equations of the first and second kind, and time fractional diffusion type equations. We consider continuity with respect to the fractional parameters as well as the initial value.     

Multiplication operators on spaces of integrable functions with respect to a vector measure

We study continuity and other properties related to some kind of compactness of multiplication operators between different spaces of pth power integrable scalar functions with respect to a vector measure.     

模糊积分变换与模糊Choquet积分的一致连续性

在一般非负单调函数空间 m[0 ,a]上引入模糊积分变换与距离的概念 ,证明了这种模糊积分变换与模糊 Choquet积分在 m[0 ,a]上关于这种距离是一致连续的 ,从而说明当 m[0 ,a]上两个函数变化不大时 ,不会使相应的模糊积分变换与模糊 Choquet积分产生较大的变化 .     

限量分配问题的一个注记

§1 引言 限量分配问题是古典概率论,组合论的重要内容。本文将文献[1]、[2]中的一类广泛的限量分配问题给以统一的处理并加以推广,归结为如下问题: 问题Ⅰ 内无序分配问题。给定m类盒和n类球,假定第i类球和第j类盒的个数分别为r_i、s_j(1≤i≤n,1≤j≤m),即所谓球的规格为(?)=(r_1,r_2,…,r_n)和盒的规格为(?)=(s_1,s_2,…,s_m)。已知第i类盒对于球的限量集为A_i(这里A_i∈N_0~t,其中每个元素表示该类盒所能容纳之球的规格,1≤i≤m),记A=(A_1,A_2,…,A_m)。则分配规格为(?)的球至规     

Integral Representations,Differentiability Properties and Limits at Infinity for Beppo Levi Functions

The first aim in the present paper is to give an integral representation for Beppo Levi functions on R ⁿ. Our integral representation is an extension of Sobolev's integral representation given for infinitely differentiable functions with compact support. As applications, continuity and differentiability properties of Beppo Levi functions are studied.Our second aim in this paper is to study the existence of limits at infinity for Beppo Levi functions. We also consider the existence of fine-type limits at infinity with respect to Bessel capacities, which yields the radial limit result at infinity.     

Local and improper Daniell-Loomis integrals

In this paper we start from previous results obtained in [7] on the abstract space of Daniell-Loomis integrable functionsL, which is constructed like to the Daniell extension process, but without continuity assumptions on the elementary integral. The localized integral is used to prove thatL consists of those functions whose local upper and lower integrals are equal and finite, or thatL is closed with respect to improper integration. Our results are also holded in integration with respect to finitely additive measures.