Functions on Linear Spaces Associated with Finite Projective Planes

Using spread sets that define finite translation planes, we construct functions that map a finite linear space into itself. Properties of such functions, which are of interest from the standpoint of cryptography, are examined. We look into the relationship between these functions and corresponding translation planes.     

The Cauchy Transform of Continuous Linear Functionals and Projections on the Weighted Spaces of Analytic Functions

Under some general assumptions on weight, we give a complete characterization of the Cauchy transform of continuous linear functionals on the weighted spaces of holomorphic functions in a ball. We construct an integral projection that sends the weighted spaces of measurable and n-harmonic functions in the ball onto the corresponding spaces of holomorphic functions.     

实赋范空间上的某些类连续线性泛函

在实赋范空间上通过范数导数（左、右两个）引进一种广义内积（上、下两个），并用它们对实赋范空间上的线性连续泛函给出上、下估计式。本文主要结果揭示了实赋范空间上的如下三类连续线性泛函的统一性。第一类连续线性泛函是指其中每一个ｆ都在闭单位球上取到其范数值ｆ。第二类连续线性泛函是指其中第一个ｆ的核Ｋｅｒ（ｆ）与另一空间元素之间的最佳逼近元存在。第三类连续性泛函是指其中每一个ｆ的上限和下限分别可用上、下两种     

On the Structure of Spaces of Polyanalytic Functions

Suppose that A_mL_p(D,) is the space of all m-analytic functions on the disk D={z:|z| < 1} which are pth power integrable over area with the weight (1-|z|²), > -1. In the paper, we introduce subspaces A_kL_p ⁰(D,), k=1,2,...,m, of the space A _mL_p(D,) and prove that A _mL_p(D,) is the direct sum of these subspaces. These results are used to obtain growth estimates of derivatives of polyanalytic functions near the boundary of arbitrary domains.     

Regularity of Continuous Linear Operators on Banach Function Spaces

In this paper we present some characterizations of Banach function spaces on which every continuous linear operator is regular.     

On the Continuity of the Generalized Nemytskii Operator on Spaces of Differentiable Functions

We obtain sufficient conditions for the continuity of the general nonlinear superposition operator (generalized Nemytskii operator) acting from the space of differentiable functions on a bounded domain to the Lebesgue space . The values of operators on a function are locally determined by the values of both the function itself and all of its partial derivatives up to order inclusive. In certain particular cases, the sufficient conditions obtained are proved to be necessary as well. The results are illustrated by several examples, and an application to the theory of Sobolev spaces is also given.     

点传递线性空间

本文是关于点传递线性空间的一个分类工作. 设${\mathcal{S}}$是一个点数为51的正则线性空间,其线长为6, $G$ 是${\cal S}$的一个自同构群.本文证明了群$G$不可能点传递.     

Embedding the Linear Structure of Planar Spaces into Projective Spaces

We show that every non-degenerate planar space with v points and planes can be embedded as a linear space into PG(3,q) for some prime power q provided that 1000( - v) v^5/6;     

Finite Linear Spaces II

Batten and Beutelspacher have characterized Finite Linear Spaces with lines of size n,n + 1 and n + 2, and with v (n + 1)²for n 22, and some of the cases for smaller n. In this article, using the structuredapproach we presented in our earlier article [8], we complete this characterization for smalln.     

On Hardy - Littlewood Maximal Functions in Orlicz Spaces

Let Φ(t) and Ψ(t) be the functions having the following representations Φ(t) = ∫a(s)ds and Ψ(t) = ∫b(s) ds, where a(s) is a positive continuous function such that ∫a(s)/s ds = + ∞ and b(s) is an increasing function such that lim_s→ ∞ b(s) = + ∞. Then the following statements for the Hardy - Littlewood maximal function M f (x) are equivalent:

• 1 (i) there exist positive constants c₁ and s₀ such that
• 1 (ii) there exist positive constant c₂ and c₃ such that

.     

关于赋范线性空间中的三类泛函方程

在赋范线性空间中考察下列几类泛函方程( ) f(x) g(y) =h(x+y) ,　 ( ) f(x+y) =f(x) f(y) ,　 ( ) f(x+y) =f(x) +f(y) +ag(x) g(y)的性质与解以及彼此之间的关系 .     

Near Polygons from Partial Linear Spaces

We construct a nondegenerate near polygon from a partial linear space without isolated points. We also prove that the points of a near polygon at distance at most 2 from a fixed point induce a near polygon, which is related to the class of the near polygons obtained from the construction. We give also a characterization of the near polygons of Hamming type in terms of parallelism.     

Angles of Norm ed Linear Spaces and Characterizations of Inner Product Spaces

§１．　Ｄｅｆｉｎｉｔｉｏｎｓ，ＬｅｍｍａｓａｎｄＴｈｅｏｒｅｍＤｅｆｉｎｉｔｉｏｎ１［１］　Ｌｅｔ（Ｘ，ｙ·ｙ）ｂｅａｒｅａｌｎｏｒｍｅｄｌｉｎｅａｒｓｐａｃｅｏｆｄｅｍｅｎｓｉｏｎｇｒｅａｔｅｒｔｈａｎ１，ｗｅｄｅｆｉｎｅａｎｇｌｅｓＡｍ，ｎ（ｘ，ｙ）ｂｅｔｗｅｅｎｎｏｎｚｅｒｏｖｅｃｔｏｒｓｘａｎｄｙｉｎＸｂｙＡｍ，ｎ（ｘ，ｙ）＝ｃｏｓ－１ｎｙｘｙｘｙ＋ｙｙｙｙｙ２－ｍｙｘｙｘｙ－ｙｙｙｙｙ２＋２（ｍ－ｎ）２（ｍ＋ｎ），ｈｅｒｅｍａｎｄｎａｒｅｔｗｏｎｏｎ－ｎｅｇｅｎｔｉｖｅｉｎｔｅ－ｇｅ…     

超积空间及其性质

引进了和内积空间没有相互包含关系的一类新空间:超积空间,进而研究了超积空间的性质.这类新的线性空间具有许多内积空间的重要性质,从而得到了线性空间一类新的度量刻画.     

Surjectivity of Linear Differential Operators in a Weighted Space of Infinitely Differentiable Functions

We present a sufficient condition for the surjectivity of a linear differential operator of infinite order with constant coefficients in a weighted space of infinitely differentiable functions on the real line.     

Banach空间中线性斜积半流指数稳定性的Holder型刻画

为了在Banach空间X的对偶空间上刻画线性斜演化半流的一致指数稳定性,借助泛函分析与算子理论得到了其一致指数稳定的一些H?lder型充要条件,所得结果推广了稳定性理论中的一些已有结论.     

On the Gap Functions of Prevariational Inequalities

Gap functions play a crucial role in transforming a variational inequality problem into an optimization problem. Then, methods solving an optimization problem can be exploited for finding a solution of a variational inequality problem. It is known that the so-called prevariational inequality is closely related to some generalized convex functions, such as linear fractional functions. In this paper, gap functions for several kinds of prevariational inequalities are investigated. More specifically, prevariational inequalities, extended prevariational inequalities, and extended weak vector prevariational inequalities are considered. Furthermore, a class of gap functions for inequality constrained prevariational inequalities is investigated via a nonlinear Lagrangian.     

线性空间上凸函数的可微性与次可微性

讨论了定义在线性空间上的广义实值凸函数的可做性和次可微性．     

On the Equivalence of Spectra of Linear Partial Differential Operators in Certain Function Spaces

For linear differential operators with coefficients of class C on ⁿ, we prove theorems on the simultaneous invertibility and equivalence of spectra in the Lebesgue space L ^p, Stepanov space M ^p, and in a particular Banach space V ^p L ^p, p 1     

Exact Values of Widths of Classes of Analytic Functions on the Disk and Best Linear Approximation Methods

In the Hardy space H _p, (p1, 0< 1, H _p,1 H _p) we develop best linear approximation methods (previously studied by Taikov and Ainulloev) for the classes W(r,,) of analytic functions on the unit disk and calculate the exact values of linear, Gelfand, and informational n-widths of these classes.