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981.
Cesàro (C,δ) means are studied for orthogonal expansions with respect to the weight function
on the unit sphere, and for the corresponding weight functions on the unit ball and the Jacobi weight on the simplex. A sharp
pointwise estimate is established for the (C,δ) kernel with δ>−1 and for the kernel of the projection operator, which allows us to derive the exact order for the norm of the Cesàro means
and the projection operator on these domains.
相似文献
982.
In this article, the authors discuss the Riemann boundary value problems with given principal part. First, authors consider a special case and give a classification of the solution class Rn by the way. And then, they consider the general case. The solvable conditions for this problem and its solutions is obtained when it is solvable. 相似文献
983.
In this survey we give a brief introduction to orthogonal polynomials, including a short review of classical asymptotic methods. Then we turn to a discussion of the Riemann-Hilbert formulation of orthogonal polynomials, and the Delft & Zhou method of steepest descent. We illustrate this new approach, and a modified version, with the Hermite polynomials. Other recent progress of this method is also mentioned, including applications to discrete orthogonal polynomials, orthogonal polynomials on curves, multiple orthogonal polynomials, and certain orthogonal polynomials with singular behavior. 相似文献
984.
985.
Xiaohong Wang Minghui Jiang Shengle Fang 《Nonlinear Analysis: Theory, Methods & Applications》2009,70(12):4294-4306
The paper discusses the global exponential stability in the Lagrange sense for a non-autonomous Cohen–Grossberg neural network (CGNN) with time-varying and distributed delays. The boundedness and global exponential attractivity of non-autonomous CGNN with time-varying and distributed delays are investigated by constructing appropriate Lyapunov-like functions. Moreover, we provide verifiable criteria on the basis of considering three different types of activation function, which include both bounded and unbounded activation functions. These results can be applied to analyze monostable as well as multistable biology neural networks due to making no assumptions on the number of equilibria. Meanwhile, the results obtained in this paper are more general and challenging than that of the existing references. In the end, an illustrative example is given to verify our results. 相似文献
986.
主要研究勒让德多项式与契贝谢夫多项式之间的关系的性质,利用生成函数和函数级数展开的方法,得出了勒让德多项式与契贝谢夫多项式之间的一个重要关系,这对勒让德多项式与契贝谢夫多项式的研究有一定的推动作用. 相似文献
987.
研究了代数多项式导数的Bernstein不等式和Markov不等式.通过代数多项式导数的一个积分表示式,给出这两个著名不等式以及它们的离散形式的证明. 相似文献
988.
The Markov–Bernstein inequalities for the Jacobi measure remained to be studied in detail. Indeed the tools used for obtaining
lower and upper bounds of the constant which appear in these inequalities, did not work, since it is linked with the smallest
eigenvalue of a five diagonal positive definite symmetric matrix. The aim of this paper is to generalize the qd algorithm
for positive definite symmetric band matrices and to give the mean to expand the determinant of a five diagonal symmetric
matrix. After that these new tools are applied to the problem to produce effective lower and upper bounds of the Markov–Bernstein
constant in the Jacobi case. In the last part we com pare, in the particular case of the Gegenbauer measure, the lower and
upper bounds which can be deduced from this paper, with those given in Draux and Elhami (Comput J Appl Math 106:203–243, 1999) and Draux (Numer Algor 24:31–58, 2000).
相似文献
989.
Stefan Kunis 《Advances in Computational Mathematics》2009,30(4):303-314
The present work considers the interpolation of the scattered data on the d-sphere by spherical polynomials. We prove bounds on the conditioning of the problem which rely only on the separation distance
of the sampling nodes and on the degree of polynomials being used. To this end, we establish a packing argument for well separated
sampling nodes and construct strongly localized polynomials on spheres. Numerical results illustrate our theoretical findings.
Dedicated to Professor Manfred Tasche on the occasion of his 65th birthday. 相似文献
990.
Charanjit S. Jutla Anindya C. Patthak Atri Rudra David Zuckerman 《Random Structures and Algorithms》2009,35(2):163-193
We present an efficient randomized algorithm to test if a given function f : ?? → ??p (where p is a prime) is a low‐degree polynomial. This gives a local test for Generalized Reed‐Muller codes over prime fields. For a given integer t and a given real ε > 0, the algorithm queries f at O( ) points to determine whether f can be described by a polynomial of degree at most t. If f is indeed a polynomial of degree at most t, our algorithm always accepts, and if f has a relative distance at least ε from every degree t polynomial, then our algorithm rejects f with probability at least . Our result is almost optimal since any such algorithm must query f on at least points. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2009 相似文献