共查询到20条相似文献,搜索用时 0 毫秒
1.
Lu Xuguang 《分析论及其应用》1996,12(4):46-66
The Cauchy’s formula of entire functions f:Ck→C is used to establish Markov-Bernstein type inequalities of multivariate polynomials with positive coeffeicients on the
k-dimensional simplex Tk⊂Rk and on the cube [0,1]k. The main results generalize and improve those of G.G. Lorentz, etc. Some applications of these inequalities are also considered
in polynomial constrained approximation. 相似文献
2.
H. N. Mhaskar 《分析论及其应用》1990,6(4):107-117
In this paper, we demonstrate how the continuity properties of the logarithmic potential of certain equilibrium measure leads
to very general polynomial inequalities. Typical inequalities considered are those which estimate the norm of the derivative
of a polynomial in terms of the norm of the polynomial itself and those which compare different norms of the same polynomial. 相似文献
3.
The Markov-Bernstein inequalities for generalized Gegenbauer weight are studied. A special basis of the vector space Pn of real polynomials in one variable of degree at most equal to n is proposed. It is produced by quasi-orthogonal polynomials with respect to this generalized Gegenbauer measure. Thanks to this basis the problem to find the Markov-Bernstein constant is separated in two eigenvalue problems. The first has a classical form and we are able to give lower and upper bounds of the Markov-Bernstein constant by using the Newton method and the classical qd algorithm applied to a sequence of orthogonal polynomials. The second is a generalized eigenvalue problem with a five diagonal matrix and a tridiagonal matrix. A lower bound is obtained by using the Newton method applied to the six term recurrence relation produced by the expansion of the characteristic determinant. The asymptotic behavior of an upper bound is studied. Finally, the asymptotic behavior of the Markov-Bernstein constant is O(n2) in both cases. 相似文献
4.
5.
The Hardy type inequality $\left( * \right) \left( {\sum\limits_{k = 1}^\infty {\frac{{\left| {\hat f\left( k \right)} \right|^p }}{{k^{2 - p} }}} } \right)^{I/p} \leqslant C_p \left\| f \right\|_{H_{ * * }^P } \left( {1/2< p \leqslant 2} \right)$ is proved for functionsf belonging to the Hardy spaceH ** p (Gm) defined by means of a maximal function. We extend (*) for 2<p<∞ when the Vilenkin-Fourier coefficients off are λ-blockwise monotone. It will be shown that under certain conditions on the Vilenkin system (in particular, for some unbounded type, too) a converse version of (*) holds also for allp>0 provided that the Vilenkin-Fourier coefficients off are monotone. 相似文献
6.
F. Peherstorfer 《Constructive Approximation》1997,13(2):261-269
We give explicitly a class of polynomials with complex coefficients of degreen which deviate least from zero on [−1, 1] with respect to the max-norm among all polynomials which have the same,m + 1, 2m ≤n, first leading coefficients. Form=1, we obtain the polynomials discovered by Freund and Ruschewyh. Furthermore, corresponding results are obtained with respect
to weight functions of the type 1/√ρl, whereρl is a polynomial positive on [−1, 1]. 相似文献
7.
8.
N. Albuquerque F. Bayart D. Pellegrino J. B. Seoane-Sepúlveda 《Israel Journal of Mathematics》2016,211(1):197-220
In this paper we obtain quite general and definitive forms for Hardy-Littlewood type inequalities. Moreover, when restricted to the original particular cases, our approach provides much simpler and straightforward proofs and we are able to show that in most cases the exponents involved are optimal. The technique we used is a combination of probabilistic tools and of an interpolative approach; this former technique is also employed in this paper to improve the constants for vector-valued Bohnenblust-Hilletype inequalities. 相似文献
9.
10.
Let p(z) be a polynomial of degree n which does not vanish in |z|<k. It is known that for each q>0 and k?1,
11.
Tamá s Erdé lyi Paul Nevai 《Transactions of the American Mathematical Society》1997,349(12):4953-4972
P. Turán [Über die Ableitung von Polynomen, Comositio Math. 7 (1939), 89-95] proved that if all the zeros of a polynomial lie in the unit interval , then . Our goal is to study the feasibility of for sequences of polynomials whose zeros satisfy certain conditions, and to obtain lower bounds for derivatives of (generalized) polynomials and Remez type inequalities for generalized polynomials in various spaces.
12.
Clément Frappier 《Journal d'Analyse Mathématique》1988,50(1):143-157
We obtain other refinements of the inequalities of S. N. Bernstein and M. Riesz for polynomials. The methods of proof use
the theory of boundpreserving convolution operators in the unit disk and interpolation formulas. 相似文献
13.
Yuan Xu 《Integral Transforms and Special Functions》2015,26(2):134-151
Orthogonal polynomials of two real variables can often be represented in complex variables. We explore the connection between the two types of representations and study the structural relations of complex orthogonal polynomials. The complex Hermite orthogonal polynomials and the disk polynomials are used as illustrating examples. 相似文献
14.
15.
Nikola Naidenov 《Analysis Mathematica》2007,33(1):55-62
There are fine extensions of the univariate Bernstein-Szeg? inequality for multivariate polynomials considered on a convex domain K. The current one estimates the gradient of the polynomial P at a point x ∈ K by constant times degree, ‖P‖ C(K) and a geometrical factor. The best constant is within [2, 2√2]. In this note we disprove the conjecture (based on some particular cases) that the best constant is 2. 相似文献
16.
M. F. Timan 《Ukrainian Mathematical Journal》1998,50(9):1473-1477
We prove the equivalence between analogs of the Paley and Nikol’skii inequalities for any orthonormal system of functions
and for almost periodic polynomials with arbitrary spectrum.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 9, pp. 1289–1292, September, 1998. 相似文献
17.
A. V. Olesov 《Siberian Mathematical Journal》2010,51(4):706-711
We sharpen and supplement the results by V. I. Smirnov, A. Aziz, and Q. M. Dawood for algebraic polynomials which generalize the classical Bernstein and Erdos-Lax inequalities. 相似文献
18.
19.
20.