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一类奇异积分方程组的样条间接近似解法 总被引:3,自引:0,他引:3
本文利用三次复插值样条函数给了定义于复平面上光滑封闭曲线上的一类奇异积分方程组(1)的一种间接近似解法,讨论了误差估计和一致收敛性。 相似文献
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多元弱奇异积分方程近似解直接方法的优化 总被引:2,自引:0,他引:2
本文研究了多元弱奇异第二类Fredholm积分方程数ψ在适应直接方法意义下的最优近似解产 们推广了文献「1」中的相关结果。 相似文献
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Stokes型积分——微分方程的Galerkin近似 总被引:2,自引:0,他引:2
张铁 《高等学校计算数学学报》1997,19(3):280-285
本文讨论一类具有Stokes方程结构的积分一微分方程的Galerkin近似,论证了近似解的存在唯一性,并分别导出速度和压力近似解的最优阶L_2模误差估计。 相似文献
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将积分区间划分为2N 等分后,我们定义了带位移的离散奇异算子■~(N).对于广义 Hilder 空间 H_(α,β,γ)中的函数 u(x),被带位移奇异算子作用后与■(N)_u 的差在分点处是 O((ln N)/(Nγ)).算子■(N)是一致有界的。利用它,我们给出了一类带位移的非线性奇异积分(哥西核)方程的离散近似解 相似文献
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Hilbert空间中算子广义逆的积分表示 总被引:2,自引:0,他引:2
利用算子矩阵分块的技巧,得到了Hilbert空间中算子的Moore-Penrose逆和Drazin逆的积分表示.给出了较为简洁的证明,同时将有限维的结论推广到无限维的情形. 相似文献
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当函数f(x,t,u)满足一些[1]中常假定的条件时,我们可借助算子S~(N)和不等式证明非线性奇异积分方程有唯一的离散近似解,这个解可用关于距离的逐次逼近法得到. 相似文献
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对于半平面中的调和函数,在本文中证明了如果它的正部满足某些限制增长条件,则它可以用半平面边界上的积分表示出来并且它的绝对值也满足类似的增长条件,这一结果改进了在半平面中调和函数的某些经典结果. 相似文献
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Jürgen Voigt 《Mathematische Nachrichten》1999,202(1):173-176
We present bounded positivity preserving operators from Lp(?) to Lq (?), for 1 < p < ∞, 1/p-1/q < 1/2, which are not integral operators. 相似文献
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星像函数的某些积分算子(英) 总被引:2,自引:0,他引:2
CertainIntegralOperatorsforStarlikeFunctionsB.A.UralegaddiC.Somanatha(Dept.ofMath.,KarnatakUniversity,Dharwad580003,India)Cer... 相似文献
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根据Beylin-Coifman-Rokhlin和Yang的观点,用合适的小波基可以刻画性地研究C.Z算子或拟微分算子,这样就可以用小波来计算算子,比如可以从奇异积分算子的B-C-R算法刻画出发,用小波限制紧算子进行逼近,本文旨在计算作为原算子与逼近算子的差的误差算子的H1到L1的连续性范数的最佳衰减速度和在Lp上的连续性范数的衰减速度的范围。 相似文献
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Gennadi Vainikko 《Numerical Functional Analysis & Optimization》2013,34(3):313-338
We study the convergence and convergence speed of two versions of spline collocation methods on the uniform grids for linear Volterra integral equations of the second kind with noncompact operators. 相似文献
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Spline Collocation-Interpolation Method for Linear and Nonlinear Cordial Volterra Integral Equations
Gennadi Vainikko 《Numerical Functional Analysis & Optimization》2013,34(1):83-109
We study the convergence and convergence speed of the discontinuous spline collocation and collocation-interpolation methods on uniform grids for linear and nonlinear Volterra integral equations of the second kind with noncompact operators. 相似文献
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本文分别讨 论了 Hardy Littlew ood 极大 算子和奇 异积分算 子的交换 子在加权 Herz 空间 ,加权 Lp空间中的 有界性 相似文献
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In this paper we are concerned with the complete spectral analysis for the operator 𝒯 = 𝒳𝒮𝒰 in the space Lp(𝕋) (𝕋 denoting the unit circle), where 𝒳 is the characteristic function of some arc of 𝕋, 𝒮 is the singular integral operator with Cauchy kernel and 𝒰 is a Carleman shift operator which satisfies the relations 𝒰2 = I and 𝒮𝒰 = ±𝒰𝒮, where the sign + or — is taken in dependence on whether 𝒰 is a shift operator on Lp(𝕋) preserving or changing the orientation of 𝕋. This includes the identification of the Fredholm and essential parts of the spectrum of the operator 𝒯, the determination of the defect numbers of 𝒯 — λI, for λ in the Fredholm part of the spectrum, as well as a formula for the resolvent operator. 相似文献
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Traditional methods of time-frequency and multiscale analysis, such as wavelets and Gabor frames, have been successfully employed
for representing most classes of pseudodifferential operators. However, these methods are not equally effective in dealing
with Fourier Integral Operators in general. In this article, we show that the shearlets, recently introduced by the authors
and their collaborators, provide very efficient representations for a large class of Fourier Integral Operators. The shearlets
are an affine-like system of well-localized waveforms at various scales, locations and orientations, which are particularly
efficient in representing anisotropic functions. Using this approach, we prove that the matrix representation of a Fourier
Integral Operator with respect to a Parseval frame of shearlets is sparse and well-organized. This fact recovers a similar
result recently obtained by Candès and Demanet using curvelets, which illustrates the benefits of directional multiscale representations
(such as curvelets and shearlets) in the study of those functions and operators where traditional multiscale methods are unable
to provide the appropriate geometric analysis in the phase space.
The second author was supported in part by a National Science Foundation grant DMS 0604561. 相似文献
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In this paper, we study the Banach algebra
generated by multidimensional pair integral operators with homogeneous kernels. We describe necessary and sufficient conditions for operators from the algebra
to be Fredholm and present a formula for calculating the index. 相似文献
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本文证明了BMO与弱核条件下Calderón-Zygmund奇异积分算子的交换子 [B,T]f=BTf-T(Bf)的L2有界性,这里B ∈BMO,T对增生的b1,b2,满足 T(b1)∈BMO,T*(b2)∈BMO,b2Tb1∈WBP. 相似文献