共查询到19条相似文献,搜索用时 93 毫秒
1.
Banach空间的接近光滑性,接近凸性和滴性及其应用 总被引:6,自引:2,他引:4
本文发现,用在一定条件下序列的相对列紧性可以统一而且十分简捷地处理Banach空间的局部接近一致光滑性,弱Hahn-Banach光滑性及滴性等概念。并由此推出了它们之间的一些新关系,得出一些新性质,也得到了Banach空间自反的一些新等价条件,在讨论了接近一致光滑和接近一致凸之间的关系的基础上,我们还得到了Bochner空间的相应一些性质。 相似文献
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置换空间PxXn中的Hahn-Banach光滑性 总被引:1,自引:0,他引:1
本文中我们给出了置换空间PxXn(弱)Hahn-Banach光滑性提升性质,它们是lp(Xn)中相应结果的推广(1<p<∞)。 相似文献
4.
林清泉 《数学物理学报(A辑)》2004,24(1):88-93
该文讨论了倒向随机微分方程Y_t=ξ+∫^T_t{g(s,Y_s,Z_s)}ds-∫^T_t{Z_s}dW_s 解在Malliavin微分意义下的光滑性.对任意的n讨论其解在Malliavin 意义下n 阶可微性,并且证明它是一个线性倒向随机微分方程的解,从而说明BSDE解的光滑性. 相似文献
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本文给出了Musielak-Orliez序列空间简洁的光滑点判据,从而得到十分便于应用的空间光滑性判别条件,同时纠正了「1」中主要定理的错误。 相似文献
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切片与Banach空间的凸性,光滑性 总被引:14,自引:1,他引:13
本文用单位球的切片统一且简捷地处理Banach空间的(局部)K一致凸、近一致凸、近一致光滑性;定义Banach空间的(局部)K一致光滑、局部近一致凸、局部近一致光滑、近-强凸、近-强光滑性等概念,并讨论上述凸性,光滑性的关系及性能。 相似文献
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本文综述满足电影型(cinematic)曲率条件的Fourier积分算子的局部光滑性及其相关研究.电影型曲率条件包含非退化条件及曲率条件.作为范例重点讨论如何通过双线性方法建立变系数版本的平方函数不等式,进而改进了Mockenhaupt-Seeger-Sogge局部光滑性的结果.与此同时,本文还分析了解决局部光滑性猜想... 相似文献
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鞅不等式与 Banach 空间的凸性和光滑性 总被引:7,自引:1,他引:7
我们用 B 值鞅的 P 方函数 S~(p)f 的 a.e.有限性刻划了 Banach 空间的p 一致可凸性质,建立了这种函数的凸Φ函数不等式,讨论了这些不等式成立的条件,鞅变换的性质以及鞅的局部收敛性与 Banach 空间的 q一致凸性和 p一致光滑性的关系,同时给出了超自反空间以及与 Hilbert 空间同构的 Banach空间的特征. 相似文献
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设(Ω,,P)是概率空间,B是Banach空间.本文引入了一类新的鞅型序列──(B值)拟终鞅型序列,并研究了它们的收敛性与Banach空间的Radon-Nikodym性,一致光滑性和UMD性的依赖关系. 相似文献
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B值鞅的加权不等式与Banach空间的凸性和光滑性 总被引:1,自引:0,他引:1
侯友良 《数学物理学报(A辑)》1993,13(1):71-79
本文对若干满足通常条件的权证明了B值鞅的加权凸Φ函数不等式和加权Davis型不等式,用这些加权不等式成立的条件刻划了Banach空间的p光滑性和q凸性,同时用B值鞅的加权不等式成立的条件给出了超自反空间以及与Hilbert空间同构的Banach空间的特征。 相似文献
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首先引入局部凸空间的k-一致极凸性和k-一致极光滑性这一对对偶概念,它们既是Banach空间k-一致极凸性和k-一致极光滑性推广,又是局部凸空间一致极凸性和一致极光滑性的自然推广.其次讨论它们与其它k-凸性(k-光滑性)之间的关系.最后,在P-自反的条件下给出它们之间的等价对偶定理. 相似文献
12.
Mehmet Ali Özarslan 《Numerical Functional Analysis & Optimization》2016,37(1):92-105
In this article, we consider modified Bernstein-Kantorovich operators and investigate their approximation properties. We show that the order of approximation to a function by these operators is at least as good as that of ones classically used. We obtain a simultaneous approximation result for our operators. Also, we prove two direct approximation results via the usual second-order modulus of smoothness and the second-order Ditzian-Totik modulus of smoothness, respectively. Finally, some graphical illustrations are provided. 相似文献
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Ioan Gavrea 《Journal of Computational Analysis and Applications》2001,3(3):249-257
We investigate the global smoothness preservation by Bernstein operators measured by second-order modulus of smoothness and give a partial answer for a conjecture raised by H. H. Gonska in 1998. 相似文献
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The present paper investigates polynomials for which the inverse inequality for moduli of smoothness holds. The technique for approach is different from the previous works for splines and is elegantly organized. 相似文献
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本文首先通过暴露集和暴露泛函的概念引入了闭凸集的紧-严格凸、紧-强凸、紧-一致凸及紧-非常凸等概念。并用对偶映射给出了Banach空间的两种新光滑性—紧-一致光滑与紧-非常光滑。然后特别研究了Banach空间的紧-非常凸与紧-非常光滑。此外还得到关于对偶映射的两个新结果。 相似文献
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George A. Anastassiou Sorin G. Gal 《Journal of Computational Analysis and Applications》1999,1(3):289-317
In this article it is established that the well-known singular integrals of Picard, Poisson–Cauchy, Gauss–Weierstrass, and their Jackson-type generalizations fulfill the global smoothness preservation property, i.e., they ripple less than the function they are applied on, that is, producing a nice and fit approximation to the unit. The related results are established over various spaces of functions and the associated inequalities involve different types of corresponding moduli of smoothness. Several times these inequalities are proved to be sharp, namely, they are attained. 相似文献
17.
在局部凸空间已有的中点局部kk-一致凸性和中点局部k-一致光滑性这一对对偶概念的基础上,证明了中点局部kk-一致凸性与中点局部(k+1)-一致凸性的关系,给出了在P-自反的条件下它们之间的等价对偶定理. 相似文献
18.
Characterization of Smoothness of Multivariate Refinable Functions in Sobolev Spaces 总被引:8,自引:0,他引:8
Rong-Qing Jia 《Transactions of the American Mathematical Society》1999,351(10):4089-4112
Wavelets are generated from refinable functions by using multiresolution analysis. In this paper we investigate the smoothness properties of multivariate refinable functions in Sobolev spaces. We characterize the optimal smoothness of a multivariate refinable function in terms of the spectral radius of the corresponding transition operator restricted to a suitable finite dimensional invariant subspace. Several examples are provided to illustrate the general theory.
19.
In recent years there have been various attempts at the
representations of {\mbox multivariate} signals such as images, which
outperform wavelets. As is well known, wavelets are not optimal in
that they do not take full advantage of the geometrical
regularities and singularities of the images. Thus these
approaches have been based on tracing curves of singularities and
applying bandlets, curvelets, ridgelets, etc., or allocating some weights to curves of
singularities like the Mumford–Shah functional and its
modifications. In the latter approach a function is approximated
on subdomains where it is smoother but there is a penalty in the
form of the total length (or other measurement) of the
partitioning curves. We introduce a combined measure of smoothness
of the function in several dimensions by augmenting its smoothness
on subdomains by the smoothness of the partitioning curves.
Also, it is known that classical smoothness spaces fail to
characterize approximation spaces corresponding to multivariate
piecewise polynomial nonlinear approximation. We show how the
proposed notion of smoothness can almost characterize these
spaces. The question whether the characterization proposed in this
work can be further simplified remains open. 相似文献