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排序方式: 共有3544条查询结果,搜索用时 15 毫秒
141.
Let μ be a finite positive Borel measure supported in [−1,1] and introduce the discrete Sobolev-type inner productwhere the mass points ak belong to [−1,1], Mk,i0, i=0,…,Nk−1, and Mk,Nk>0. In this paper, we study the asymptotics of the Sobolev orthogonal polynomials by comparison with the orthogonal polynomials with respect to the measure μ and we prove that they have the same asymptotic behaviour. We also study the pointwise convergence of the Fourier series associated to this inner product provided that μ is the Jacobi measure. We generalize the work done by F. Marcellán and W. Van Assche where they studied the asymptotics for only one mass point in [−1,1]. The same problem with a finite number of mass points off [−1,1] was solved by G. López, F. Marcellán and W. Van Assche in a more general setting: they consider the constants Mk,i to be complex numbers. As regards the Fourier series, we continue the results achieved by F. Marcellán, B. Osilenker and I.A. Rocha for the Jacobi measure and mass points in
. 相似文献
142.
Let be a bounded domain such that . We obtain existence of sign-changing solutions for the Dirichlet problem on Ω,u=0 on ∂Ω for suitable positive numbers μ and λ. 相似文献
143.
Wei-Shyan Tai 《Proceedings of the American Mathematical Society》2001,129(3):699-711
In this paper a capacitary weak type inequality for Sobolev functions is established and is applied to reprove some well-known results concerning Lebesgue points, Taylor expansions in the -sense, and the Lusin type approximation of Sobolev functions.
144.
Gancho Tachev 《Journal of Computational Analysis and Applications》2001,3(4):361-381
A direct theorem for approximation by algebraic polynomials in two variables with different degrees in each variable in Lp-metric (1 p ) on rectangles is proved, and the dependence of the constants on various parameters is studied. 相似文献
145.
A non-conforming finite element method with anisotropic mesh grading for the Stokes problem in domains with edges 总被引:5,自引:0,他引:5
The solution of the Stokes problem in three-dimensional domainswith edges has anisotropic singular behaviour which is treatednumerically by using anisotropic finite element meshes. Thevelocity is approximated by CrouzeixRaviart (nonconformingP1 ) elements and the pressure by piecewise constants. Thismethod is stable for general meshes (without minimal or maximalangle condition). Denoting by Ne the number of elements in themesh, the interpolation and consistency errors are of the optimalorder h Ne1/3 which is proved for tensor product meshes.As a by-product, we analyse also nonconforming prismatic elementswith P1 [oplus ] span {x32} as the local space for the velocitywhere x3 is the direction of the edge. 相似文献
146.
A new a posteriori L2 norm error estimator is proposed for thePoisson equation. The error estimator can be applied to anisotropictetrahedral or triangular finite element meshes. The estimatoris rigorously analysed for Dirichlet and Neumann boundary conditions. The lower error bound relies on specifically designed anisotropicbubble functions and the corresponding inverse inequalities.The upper error bound utilizes non-standard anisotropic interpolationestimates. Its proof requires H2 regularity of the Poisson problem,and its quality depends on how good the anisotropic mesh resolvesthe anisotropy of the problem. This is measured by a so-calledmatching function. A numerical example supports the anisotropic error analysis. 相似文献
147.
Jos M. Rodríguez 《Journal of Approximation Theory》2001,108(2):119
We characterize the set of functions which can be approximated by polynomials with the following norm
for a big class of weights w0, w1, …, wk 相似文献
Full-size image
148.
Cooper对质心定向运动速度的空间分布规律及“邻近效应” 总被引:3,自引:0,他引:3
在零场下 ,由超导电流密度的两种表达形式 ,导出了超导载流子质心定向运动速度的空间分布规律 ,并由毕萨定律定性地解释了“邻近效应” 相似文献
149.
A nonlinear integral operator T of the form (Tf)(s)=∫G K(t, f (σ(s, t))) dμ(t), for sG, is defined and investigated in the measure space (G, Σ, μ), where f and K are vector-valued functions with values in normed linear spaces E and F, respectively. The results are applied to the case of integro-differential operators in generalized Orlicz–Sobolev spaces. There are studied problems of existence, embeddings, and approximation by means of T. 相似文献
150.
In this paper, we study orthogonal polynomials with respect to the bilinear form (f, g)
S
= V(f) A
V(g)
T
+ <u, f
(N)
g
(N)V(f) =(f(c
0), f "(c
0), ..., f
(n – 1)
0(c
0), ..., f(c
p
), f "(c
p
), ..., f
(n – 1)
p(c
p
))
u is a regular linear functional on the linear space P of real polynomials, c
0, c
1, ..., c
p
are distinct real numbers, n
0, n
1, ..., n
p
are positive integer numbers, N=n
0+n
1+...+n
p
, and A is a N × N real matrix with all its principal submatrices nonsingular. We establish relations with the theory of interpolation and approximation. 相似文献