关于Hilbert积分不等式新的改进和推广

本文通过引入一些常数，运用一些分析技巧和Young不等式，给出了Hilbert积分不等式的一些新的改进和推广。     

关于新型Hilbert不等式的积分形式

本文利用分析的方法及不等式理论，建立了两个新型Hilbert不等式的积分形式，获得了一些新结果，推广了某些相关的结果．     

关于弦幂积分的一个不等式

首先利用Hlder不等式证明一个弦幂积分不等式,然后利用该不等式获得了一个类似于Maclaurin的弦幂积分不等式.     

关于L2空间中的Bernstein-MarkoV不等式

纠正了闵国华（１９９２年）关于Ｌ＾２空间中的Ｂｅｒｎｓｔｅｉｎ－Ｍａｒｋｏｖ不等式的几个错误结果。     

关于一个Hilbert类不等式及其应用

本文给出一个具有同样最佳常数π的Hilbert类不等式。作为应用，建立其等价形式及导出一些特殊的结果。     

基本Bernstein多项式的一个积分不等式(英文)

本文研究了Bernstein多项式.通过归纳法,建立了一个与基本Bernstein多项式有关的积分型不等式.     

关于二阶导数的若干新积分不等式

根据Cauchy-Schwarz不等式,得到了C2([a,b])空间中函数的二阶导数的若干新积分不等式.     

Hardy-Hilbert型积分不等式的一个改进及其应用

本利用改进了的H（oe）lder’s不等式对一个类似于Hardy—Hilbert不等式的不等式作了进一步改进。     

关于Szeg?的一个不等式

设P_n(x)为[0,∞)上次数不超过n的代数多项式,则有‖p′_n(x)e^-x‖_[0,∞)≤(6.3n+1)‖p_n(x)e^-x‖_[0,∞).若p_n(x)同时又是奇函数或偶函数,则有‖p′_n(x)e^-x‖_[0,∞)≤(1.8+7n^1/2)‖p相似文献   

Local behaviour of polynomials

In this paper we study the local behaviour of a trigonometric polynomial around any of its zeros in terms of its estimated values at an adequate number of freely chosen points in . The freedom in the choice of sample points makes our results particularly convenient for numerical calculations. Analogous results for polynomials of the form are also proved.

     

On random algebraic polynomials

This paper provides asymptotic estimates for the expected number of real zeros and -level crossings of a random algebraic polynomial of the form , where are independent standard normal random variables and is a constant independent of . It is shown that these asymptotic estimates are much greater than those for algebraic polynomials of the form .

     

On algebraic polynomials with random coefficients

The expected number of real zeros and maxima of the curve representing algebraic polynomial of the form

where , are independent standard normal random variables, are known. In this paper we provide the asymptotic value for the expected number of maxima which occur below a given level. We also show that most of the zero crossings of the curve representing the polynomial are perpendicular to the axis. The results show a significant difference in mathematical behaviour between our polynomial and the random algebraic polynomial of the form which was previously the most studied.

     

Some integral mean estimates for polynomials

In this paper we establish Lq inequalities for polynomials, which in particular yields interesting generalizations of some Zygmund-type inequalities.     

Numerical solution of some classes of integral equations using Bernstein polynomials

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(Shifted) Macdonald polynomials: q-Integral representation and combinatorial formula

We extend some results about shifted Schur functions to the general context of shifted Macdonald polynomials. We strengthen some theorems of F. Knop and S. Sahi and give two explicit formulas for these polynomials: a q-integral representation and a combinatorial formula. Our main tool is a q-integral representation for ordinary Macdonald polynomial. We also discuss duality for shifted Macdonald polynomials and Jack degeneration of these polynomials.     

New integral mean estimates for polynomials

In this paper we prove someL ^P inequalities for polynomials, wherep is any positive number. They are related to earlier inequalities due to A Zygmund, N G De Bruijn, V V Arestov, etc. A generalization of a polynomial inequality concerning self-inversive polynomials, is also obtained.     

Some families of hypergeometric polynomials and associated integral representations

The main object of this paper is to investigate several general families of hypergeometric polynomials and their associated single-, double-, and triple-integral representations. Some known or new consequences of the general results presented here, involving such classical orthogonal polynomials as the Jacobi, Laguerre, Hermite, and Bessel polynomials, and various other relatively less familiar hypergeometric polynomials, are also considered. Each of the integral representations, which are derived in this paper, may be viewed also as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials.     

Integral representation of holomorphic functions on Banach spaces

In this paper we discuss the problem of integral representation of analytic functions over a complex Banach space E. We obtain, for a wide class of functions, integral representations of the form