Baskakov型算子同时逼近的点态估计

In this paper, for Baskakov, Baskakov-Kantorovich and Baskakov-Durrmyer operators Ln(f,x),we give a simultaneous approximation of equivalent theorem with ω^2ψλ (f, t) The theorem unites the corrosponding results of classical and the Ditzian-Totik moduli of smoothness.     

Szaesz型算子同时逼近的点态估计

关于Ｓｚａｅｓｚ型算子的线性组合，李秉政「４」给出了同时逼近的点态结果，本文将应用光滑模ωψ＾λ（ｆ，ｔ）推广这些结果。     

Bernstein算子线性组合同时逼近的点态估计

借助于光滑模ωψ^rλ（f,t）（0≤λ≤1）给出了Bernstein算子线性组合同时逼近的点态结果。     

修正的Bernstein-Durrmeyer算子的同时逼近

本文的目的是证明修正的Bernstein-Durrmeyer算子同时逼近的正逆定理,在点态意义下,我们得到了一个同时逼近的等价特征刻画。     

多元Stancu算子的Boolean和迭代

定义单纯形上高维Stancu算子的Boolean和迭代算子并且研究它逼近连续函数的正定理、逆定理与饱和定理，得到了较高的逼近阶．     

Bernstein型算子同时逼近误差

该文证明了C[0,1]空间中的函数及其导数可以用Bernstein算子的线性组合同时逼近,得到逼近的正定理与逆定理.同时,也证明了Bernstein算子导数与函数光滑性之间的一个等价关系.该文所获结果沟通了Bernstein算子同时逼近的整体结果与经典的点态结果之间的关系.     

算子的点态逼近

本文应用Ditzian-Totik模得到Baskakov-Durrmeyer算子线性组合的点态逼近的等价定理.     

Bernstein-Kantorovich算子导数的逼近

给出了Bernstein-Kantorovich算子的导数和光滑模之间的关系及它们的线性组合的逼近等价定理.     

Bernstein型算子加Jacobi权逼近

对于Bernstein型算子,证明它在通常的加权范数下是无界的,通过引进新的加权范数,研究其加Jacobi权的逼近性质,得到加权逼近的正逆定理,从而导出加权逼近特征的等价刻画．     

一类推广的Bernstein-Kantorovich算子的点态逼近

讨论Bernstein-Kantorovich算子的一种推广形式的逼近性质,运用插项的方法证明了逼近正定理,并证明了逆定理,得到了逼近等价定理.完善了算子在逼近性质方面的结果.     

On pointwise estimates for the Littlewood-Paley operators

In a recent paper we proved pointwise estimates relating some classical maximal and singular integral operators. Here we show that inequalities essentially of the same type hold for the Littlewood-Paley operators.

     

On the eigenvalues of the Sturm-Liouville operator with potentials from Sobolev spaces

We study the asymptotic behavior of the eigenvalues the Sturm-Liouville operator Ly = ?y″ + q(x)y with potentials from the Sobolev space W ₂ ^θ?1 , θ ≥ 0, including the nonclassical case θ ∈ [0, 1) in which the potential is a distribution. The results are obtained in new terms. Let s _2k (q) = λ _k ^1/2 (q) ? k, s _2k?1(q) = μ _k ^1/2 (q) ? k ? 1/2, where {λ _k } ₁ ^∞ and {μ _k } ₁ ^∞ are the sequences of eigenvalues of the operator L generated by the Dirichlet and Dirichlet-Neumann boundary conditions, respectively,. We construct special Hilbert spaces t ₂ ^θ such that the mapping F:W ₂ ^θ?1 →t ₂ ^θ defined by the equality F(q) = {s _n } ₁ ^∞ is well defined for all θ ≥ 0. The main result is as follows: for θ > 0, the mapping F is weakly nonlinear, i.e., can be expressed as F(q) = Uq + Φ(q), where U is the isomorphism of the spaces W ₂ ^θ?1 and t ₂ ^θ , and Φ(q) is a compact mapping. Moreover, we prove the estimate ∥Ф(q)∥_τ ≤ C∥q∥_θ?1, where the exact value of τ = τ(θ) > θ ? 1 is given and the constant C depends only on the radius of the ball ∥q∥_θ? ≤ R, but is independent of the function q varying in this ball.     

Estimates of the derivatives for parabolic operators with unbounded coefficients

We consider a class of second-order uniformly elliptic operators with unbounded coefficients in . Using a Bernstein approach we provide several uniform estimates for the semigroup generated by the realization of the operator in the space of all bounded and continuous or Hölder continuous functions in . As a consequence, we obtain optimal Schauder estimates for the solution to both the elliptic equation (0$">) and the nonhomogeneous Dirichlet Cauchy problem . Then, we prove two different kinds of pointwise estimates of that can be used to prove a Liouville-type theorem. Finally, we provide sharp estimates of the semigroup in weighted -spaces related to the invariant measure associated with the semigroup.

     

半线性方程周期边值问题

本文利用整体反函数理论，研究了半线性周期边值问题，给出存在唯一性的充分条件，推广和改进了现有的结果。     

Simultaneous approximation for Szász-Mirakian quasi-interpolants

We obtain simultaneous approximation equivalence theorem for Száz-Mirakian quasi-interpolants.     

Bernstein-Sikkema-Bézier算子的点态逼近

讨论了Bernstein-Sikkema-Bézier算子点态逼近的等价定理,首先利用插项的的方法证明了正定理,然后应用讨论算子逼近的常规方法给出了其逼近的逆定理.