共查询到20条相似文献,搜索用时 15 毫秒
1.
Chun-Yan Li 《Complex Analysis and Operator Theory》2012,6(1):1-21
In this paper, operator Bessel sequences, operator frames, Banach operator frames, Operator Riesz bases for Banach spaces
and dual frames of an operator frame are introduced and discussed. The necessary and sufficient condition for a Banach space
to have an operator frame, a Banach operator frame or an operator Riesz basis are given. In addition, operator frames and
operator Riesz bases are characterized by the analysis operator of operator Bessel sequences. 相似文献
2.
非线性Lipschitz算子的Lipschitz对偶算子及其应用 总被引:3,自引:0,他引:3
在文山中我们对非线性Lipschitz算子定义了其Lipschitz对偶算子,并证明了任意非线性Lipschitz算子的Lipschitz对偶算子是一个定义在Lipschitz对偶空间上的有界线性算子.本文还进一步证明:设C为 Banach空间 X的闭子集,C*L为C的 Lipschitz对偶空间,U为 C*L上的有界线性算子,则当且仅当 U为 w*-w*连续的同态变换时,存在Lipschitz连续算子T,使U为T的Lipschitz对偶算子.这一结论的理论意义在于:它表明一个非线性Lipschitz算子的可逆性问题可转化为有界线性算子的可逆性问题.作为应用,通过引入一个新概念──PX-对偶算子,在一般框架下给出了非线性算子半群的生成定理. 相似文献
3.
Elina Shishkina 《Mathematical Methods in the Applied Sciences》2019,42(15):5060-5071
The paper is devoted to the study of the fractional integral operator, which is a negative real power of the singular wave operator generated by Bessel operator using weighted generalized functions. We give conditions for this operator to be bounded in appropriate spaces, obtain formula for the Hankel transform of this operator, and get formula of connection between this operator and natural degree of singular wave operator generated by Bessel operator. 相似文献
4.
In this paper, a positive operator is given. It is shown that the product of this positive operator and the convolution operator is a trace class Hilbert-Schmidt integral operator and has nonnegative eigenvalues. A formula is given for the trace of this product operator. It seems that this product operator is the closest trace class integral operator which has nonnegative eigenvalues and is related to the Weil distribution in the context of Connes’ program for the Riemann hypothesis. A relation is given between the trace of the product operator and the Weil distribution.
相似文献5.
类似与标型谱算子,U-标算子是否拟仿射相似于自伴算子是一“公开问题”.尽管对具纯离散谱的U-标算子答案是肯定的,但一般情况下并不成立.本文继续探讨这一问题,证明了U-标算子在一强范数拓扑意义下是Hermite算子,或者说U-标算子拟仿射相似于Hermite算子,并给出U-标算子是标型谱算子的充要条件. 相似文献
6.
New sharp multiplicative reverses of the operator means inequalities are presented, with a simple discussion of squaring an operator inequality. As a direct consequence, we extend the operator Pólya-Szegö inequality to arbitrary operator means. Furthermore, we obtain some new lower and upper bounds for the Tsallis relative operator entropy, operator monotone functions and positive linear maps. 相似文献
7.
在本文中我们研究了由具有弱(p,p)型和(∞,∞)型的鞅算子T所推广鞅Orlicz空间,而鞅算子T是经典鞅论中极大算子M和均方算子S的推广.为了说明具有弱(p,p)型和(∞,∞)型的鞅算子T的存在性,我们引进了鞅算子Mp.利用鞅算子Mp,我们得到了鞅算子的双Φ不等式的最优条件,而且我们还得到了鞅算子Mp的Doob不等式. 相似文献
8.
S. N. Mishin 《Russian Mathematics (Iz VUZ)》2018,62(11):28-44
We consider a general method of solving equations whose left-hand side is a series by powers of a linear continuous operator acting in a locally convex space. Obtained solutions are given by operator series by powers of the same operator as the left-hand side of the equation. The research is realized by means of characteristics (of order and type) of operator as well as operator characteristics (of operator order and operator type) of vector relatively of an operator. In research we also use a convergence of operator series on equicontinuous bornology. 相似文献
9.
Fuzhen Zhang 《Journal of Mathematical Analysis and Applications》2007,333(2):1264-1271
This paper is focused on the operator inequalities of the Bohr type. We will give a new and transparent proof for the operator Bohr inequality through an absolute value operator identity, show some related operator inequalities by means of 2×2 (block) operator matrices, and finally we will present a generalization of the operator Bohr inequality for multiple operators. 相似文献
10.
研究了两部件并联维修系统算子的性质,通过选取空间和定义算子将模型方程转化成了抽象柯西问题,证明了系统算子是定义域稠的预解正算子,0是系统算子的几何重数为1的本征值.讨论了系统算子的共轭算子及其定义域,证明了0是共轭算子的代数重数为1的特征值. 相似文献
11.
12.
In this paper, we introduce the notions of multiplier, -closure operator and modal operator on hoop-algebras. After that, we investigate some algebraic properties of multiplier, -closure operator and modal operator on hoop-algebras. Then we study relationships between multiplier and closure operator on hoop-algebras showing that, any monotone modal operator on hoop-algebra serves as a closure operator. Finally we represent image of hoop-algebra under the closure operator can be a hoop-algebra. 相似文献
13.
The recursion operator of the Kadomtsev-Petviashvili equation is algorithmically derived. This recursion operator is the two-spatial-dimensional analogue of the Lenard operator of the Korteweg-deVries equation. It is also the “squared” eigenfunction operator of the time-dependent Schrödinger operator. The existence of the recursion operator suggests that the Kadomtsev-Petviashvili equation is a hi-Hamiltonian system. 相似文献
14.
15.
We present a new aggregation operator called the generalized ordered weighted exponential proportional averaging (GOWEPA) operator, which is based on an optimal model. We study some properties and different families of the GOWEPA operator. We also generalize the GOWEPA operator. The key advantage of the GOWEPA operator is that it is an aggregation operator with theoretic basis on aggregation. Moreover, we propose an orness measure of the GOWEPA operator and indicate some properties of this orness measure. Furthermore, we introduce the least exponential squares method (LESM) to determine the GOWEPA operator weights based on its orness measure. In the end, we develop an application of the new approach in a case of group decision making in investment selection. 相似文献
16.
A. I. Perov 《Functional Analysis and Its Applications》2017,51(4):310-315
In a generalization of Fiedler’s theorem, a block condition for the invertibility of an operator and an estimate for the operator matrix of the inverse operator are presented. A block condition for an operator to be Hurwitz is also given, which contains an estimate of the spectral abscissa of the operator. 相似文献
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18.
姜玉秋 《数学的实践与认识》2009,39(3)
算子群作为群的推广,算子群在群论里有许多应用.类似地,作为算子群和李代数的推广,算子李代数将会有许多应用.给出了算子李代数的一些性质,得到了算子李代数半单性的充分必要条件.同时得到算子李代数半单性与非退化killing型的关系. 相似文献
19.
研究了两相同部件冷贮备可修系统算子性质,此系统由2个同型部件及一个修理设备构成.其中一个部件工作,另一个部件冷储备.运用C_0半群的理论,证明了系统算子是稠定的预解正算子,得出了系统算子的共轭算子及其定义域,并证明了系统算子的增长界为0.最后运用了预解正算子中共尾的概念及相关理论,证明了系统算子的谱上界也是0. 相似文献
20.
Xinwang Liu 《International Journal of Approximate Reasoning》2010,51(3):305-334
The paper first summarizes the orness measures and their common characteristics of some averaging operators: the quasi-arithmetic mean, the ordered weighted averaging (OWA) operator, the regular increasing monotone (RIM) quantifier and the weighted function average operator, respectively. Then it focuses on the aggregation properties and operator determination methods for two kinds of quasi-arithmetic mean-based compound aggregation operators: the quasi-OWA (ordered weighted averaging) operator and the Bajraktarevi? mean. The former is the combination of the quasi-arithmetic mean and the OWA operator, while the latter is the combination of the quasi-arithmetic mean and the weighted function average operator. Two quasi-OWA operator forms are given, where the OWA operator is assigned directly or generated from a RIM (regular increasing monotone) quantifier indirectly. The orness indexes to reflect the or-like level of the quasi-OWA operator and Bajraktarevi? mean are proposed. With generating function techniques, the properties of the quasi-OWA operator and Bajraktarevi? mean are discussed to show the rationality of these orness definitions. Based on these properties, two families of parameterized quasi-OWA operator and Bajraktarevi? mean with exponential and power function generators are proposed and compared. It shows that the method of this paper can also be applied to other function-based aggregation operators. 相似文献