1) Riesz transform
Riesz变换
1.
The boundedness of commutators [b,T] generated by Riesz transform associated with Schrdinger operator.
研究了与薛定谔算子相关的Riesz变换和齐次Lipschitz函数组成的交换子的有界性问题。
2.
In this paper, we consider the L~p boundedness of generalized Riesz transformassociated with nondivergent elliptic operators, and solve by means of wavelets theprobelm about the L~p (2≤p<∞) boundedness of Riesz transform under the conditionthat its BMO norm of coefficients is small enough.
本文利用小波方法在一般阶的非散度椭圆算子的系数BMO模非常小的情形下,证明了广义 Riesz变换的 L~p(2≤p<+∞)有界性。
3.
In this paper we consider the boundedness of Riesz transform associated touniformly elliptic operators L =--div(A(x)) + V(x) with non-negative potentials V onR~n which belonging to certain reverse Holder class.
本文主要讨论了当非负位势 V(x)属于某逆Holder类时,由一致椭圆算子L=-div(A(x))+V(x)所定义的 Riesz变换在 L~p空间的有界性。
2) maximal Riesz transforms
极大Riesz变换
1.
BLO_L(R~n) estimates for maximal Riesz transforms associated with Schrdinger operators,Hardy-Littlewood maximal operator and natural maximal operator are obtained.
与薛定谔算子相关的极大Riesz变换,Hardy-Littlewood极大算子和自然极大算子的BLO_L(R~n)估计被得到。
3) Riesz transform associated with Schr(o|¨)dinger operator
薛定谔算子决定的Riesz变换
4) Riesz potential of variable order
变阶Riesz位势
1.
Riesz potential of variable order Lipschitz function of variable order in Homogeneous space are defined.
在齐型空间中引入变阶Riesz位势和变阶Lipshitz函数,并研究了变阶Riesz位势的变阶Lipshitz性质。
5) Riesz potential integral operator of variable order
变阶Riesz位势型积分算子
6) riesz bases
Riesz基
1.
Riesz bases in L~2(0,1)~2 related to sampling in 2-dimenional wavelet subspace;
基于L~2(0,1)~2空间Riesz基的二维小波子空间采样定理
2.
Starting with a pair of compactly supported refinable functions φ and in L~2(R) satisfying a very mild condition,a general principle for constructing a wavelet ψ of dilation factor a is provided such that the wavelets ψ_(jk)=a~(j2)ψ(a~j·-k)(j,k∈Z) form a Riesz bases for L~2(R).
-k)(j,k∈Z)构成L2(R)的Riesz基,当φ属于Sobolev空间Hm(R)的时,导数aj2ψ(m)(aj。
3.
Let {x_n} be a Riesz bases of Banach space X and T:X→X be a linear homeomorphism and a bounded linear operator,if there exist M≥0,A>0,β≥0,that enableA>(βA+M)‖T‖,and {y_n} satisfies‖∑c_ny_n‖≤β‖∑c_nx_n‖+M‖c‖for any c={c_n}∈l~2,{x_n+T(y_n)} is also a Riesz base of X.
利用泛函分析中的线性同胚及有界线性算子理论,研究Banach空间中Riesz基的稳定性问题。
补充资料：Radon变换和逆Radon变换
Radon变换和逆Radon变换
X线物理学术语。CT重建图像成像的主要理论依据之一。1917年澳大利亚数学家Radon首先论证了通过物体某一平面的投影重建物体该平面两维空间分布的公式。他的公式要求获得沿该平面所有可能的直线的全部投影(无限集合)。所获得的投影集称为Radon变换。由Radon变换进行重建图像的操作则称为逆Radon变换。Radon变换和逆Radon变换对CT成像的意义在于，它从数学原理上证实了通过物体某一断层层面“沿直线衰减分布的投影”重建该层面单位体积，即体素的线性衰减系数两维空间分布的可能性。
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参考词条