一类多元函数极限不存在性判别法

为一类二元及三元广义齐次有理分式函数极限的不存在性建立一个判别准则.     

Interpolation Formula for Functions of Several Variables

Mathematical Notes -     

Some Polynomial Expansions for Functions of Several Variables

In the present paper three new expansion formulae are givenfor a function of several variables, which is defined by a multiplepower series with arbitrary terms. It is also indicated howthese general results can be applied to derive various knownor new multiplication theorems for certain hypergeometric functionsof one and more variables.     

Estimate for the Best Approximation of Summable Functions of Several Variables with a Certain Symmetry of Fourier Coefficients

An upper bound for the best approximation of summable functions of several variables by trigonometric polynomials in the metric of L is determined in terms of Fourier coefficients. We consider functions representable by trigonometric series with certain symmetry of coefficients satisfying a multiple analog of the Sidon–Telyakovskii conditions.     

The Fourier Formula for Discontinuous Functions of Several Variables

An analog of the classical Fourier formula for the characteristic function of a convex compact set is considered:

p-adic Transcendence and p-adic Transcendence Measures for the Values of Mahler Type Functions

We prove the p-adic transcendence and p-adic transcendence measures for the values of some Mahler type functions.     

Some Extension Theorems for Regular Functions of Several Quaternionic Variables

In this paper we study the extension theorems for solutions of inhomogeneous Cauchy-Fueter system. In particular cases, we obtain the extension theorems for regular functions of several quaternionic variables. At the end of the paper we give some applications of these theorems.     

多元函数的可微性

给出了多元函数可微性的等价条件 ;利用这个条件可以简便有效地判别多元函数的可微性     

关于多元幂级数

引入了多元函数项级数的概念,给出了其收敛域及和函数的定义;通过详实的例子讨论了多元幂级数的收敛域、和函数及多元函数展开为多元幂级数的计算方法.     

On the Transcendence of Infinite Sums of Values of Rational Functions

Convergent sums and , where P(X), Q(X) Q[X], and Q(X)has only simple rational roots, are investigated. Adhikari,Shorey and the authors have shown that T and U are either rationalor transcendental. Simple necessary and sufficient conditionsare formulated for the transcendence of T and U if the degreeof Q is 3 and 2, respectively.     

On Extremal Properties of Interpolation Polynomials for Functions of Several Variables

By using earlier results, we find solutions of two extremal problems on sets of interpolation polynomials for functions of several variables.     

Bloch Functions in Several Complex Variables, I

Bloch functions on the unit disk are those analytic functionsf for which the quantity |f'(z)|(1 – |z|²) is bounded(for z in the disk). In this paper, Bloch functions on boundedhomogeneous domains in complex m-space are studied. The mainresult shows that many of the equivalent definitions of Blochfunctions on the unit disk are also equivalent in the generalsetting. Current Address: 39 Trinity College, Dublin 2, Ireland.     

Hyperplane Singularities of Analytic Functions of Several Complex Variables

A new class of non-isolated singularities called hyperplane singularities is introduced. Special deformations with simplest critical points are constructed and an algebraic expression for the number of Morse points is given. The topology of the Milnor fibre is completely studied.     

Approximation of Classes of Periodic Functions in Several Variables

We study the approximation of the classes and of periodic functions of several variables by multiple Fourier sums of fixed order constructed with regard to individual properties of functions from these classes. In a number of cases, such approximations allow us to achieve a better degree of approximation of the classes indicated above as compared to their approximation by staircase hyperbolic Fourier sums.     

微分几何观点下二元函数的极值

利用曲面的局部微分性质给出二元函数极值存在的必要条件和充分条件,并将之运用于具有明显几何特征的曲面对应的二元函数极值的判别问题中.     

Boundedness of L-Index for the Composition of Entire Functions of Several Variables

Ukrainian Mathematical Journal - We consider the following compositions of entire functions $$ F(z)=fleft(varPhi (z)right)kern0.5em mathrm{and}kern0.5em...     

Arithmetic Properties of Solutions of Certain Functional Equations in Several Variables

We consider the linear independence of the values of solutions of certain functional equations in several variables. As an application we obtain a quantitative refinement of a certain result of Bézivin.