共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
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
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.
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
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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
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文章研究一个带有贝努利反馈且系统服务台经常遭受启动故障的重新访问排队系统模型,利用线性算子半群理论,通过对描述其系统行为的偏微分方程组的研究,证明了该模型所描述的系统所确定的算子是闭稠定耗散算子,生成C0压缩半群,从而得到系统的适定性.在证明1是算子的预解点时,采用了共轭方法. 相似文献
9.
本文主要研究 2 × 2 算子矩阵的正性,并利用极大Tseng逆理论等给出了 2 × 2 算子矩阵为正算子的等价条件.此外, 给出一类正算子矩阵的平方根算子表达式. 相似文献
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Estimates for restrictions of monotone operators on the cone of decreasing functions in Orlicz space
M. L. Goldman 《Mathematical Notes》2016,99(1-2):24-36
We introduce a number of notions related to the Lyapunov transformation of linear differential operators with unbounded operator coefficients generated by a family of evolution operators. We prove statements about similar operators related to the Lyapunov transformation and describe their spectral properties. One of the main results of the paper is a similarity theorem for a perturbed differential operator with constant operator coefficient, an operator which is the generator of a bounded group of operators. For the perturbation, we consider the operator ofmultiplication by a summable operator function. The almost periodicity (at infinity) of the solutions of the corresponding homogeneous differential equation is established. 相似文献
12.
A system of ordinary differential equations of mixed order on an interval (0, r0) is considered, where some coefficients are singular at 0. Special cases have been dealt with by Kako , where the essential spectrum of an operator associated with a linearized MHD model was calculated, and more recently by Hardt , Mennicken and Naboko . In both papers this operator is a selfadjoint extension of an operator on sufficiently smooth functions. The approach in the present paper is different in that a suitable operator associated with the given system of ordinary differential equations is explicitly defined as the closure of an operator defined on sufficiently smooth functions. This closed operator can be written as a sum of a selfadjoint operator and a bounded operator. It is shown that its essential spectrum is a nonempty compact subset of ℂ, and formulas for the calculation of the essential spectrum in terms of the coefficients are given. 相似文献
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An exponentially convergent approximation to the solution of a nonlinear first order differential equation with an operator coefficient in Banach space is proposed. The algorithm is based on an equivalent Volterra integral equation including the operator exponential generated by the operator coefficient. The operator exponential is represented by a Dunford-Cauchy integral along a hyperbola enveloping the spectrum of the operator coefficient, and then the integrals involved are approximated using the Chebyshev interpolation and an appropriate Sinc quadrature. Numerical examples are given which confirm theoretical results.
15.
传统的微分方程的方法是利用Taylor展开用主象征逼近象征;本文用充分好的紧算子来逼近象征算子,并且逼近算子在算子范数意义下快速逼近原来的算子. 相似文献
16.
Yehui Peng Zhenhai Liu Heying Feng 《Journal of Applied Mathematics and Computing》2010,34(1-2):233-250
A modified iteratively regularized gradient method and its continuous version are proposed for nonlinear ill-posed problems, in which the Tikhonov regularization term is generated by a linear operator. The linear operator may have some physical meaning. And by employing the linear operator, scaling the problem can be avoided in the case that the nonlinear operator in the problem has larger gradient. Adopting a posteriori and a priori stopping rule respectively, we establish the convergence results by using a modified approximate source condition. The numerical results show that the linear operator effects the performance greatly. 相似文献
17.
In a Morrey space, the product of the convolution operator with summable kernel and the operator of multiplication by an essentially bounded function is considered. Sufficient conditions for such a product to be compact are obtained. In addition, it is shown that the commutator of the convolution operator and the operator of multiplication by a function of weakly oscillating type is compact in a Morrey space. 相似文献
18.
We consider a self-adjoint differential operator in Hilbert space. Then the domain of the operator is changed by the perturbation of the boundary conditions so that a given neighborhood “is cleared” from the points of the spectrum of the perturbed operator. For the Sturm–Liouville operator on the segment and the Laplace operator on the square such a possibility is attained via integral perturbations of boundary conditions. 相似文献
19.
研究了两同型部件温贮备可修系统,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,另一个部件温储备.运用C_o半群的理论,证明系统算子是稠定的预解正算子,得出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O.最后运用了预解正算子中共尾的概念及相关理论,证明系统算子的谱上界也是0. 相似文献
20.
R. S. Ismagilov 《Theoretical and Mathematical Physics》2014,180(1):753-758
We consider a locally compact nonconnected nondiscrete field and study a linear operator given by the sum of the operator of multiplication by a function and the operator of convolution with a generalized function. We derive the asymptotic form of the spectrum of that linear operator. In this problem, we use the generalized p-adic Feynman-Kac formula. 相似文献