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1.
We prove that the Markov operator associated to an iterated function system consisting of φ-max-contractions with probabilities has a unique invariant measure whose support is the attractor of the system.  相似文献   

2.
In this paper, we first give the definition of possibly non-unital function system, which is a characterization of the self-adjoint subspace of the space of continuous functions on a compact Hausdorff space with the induced order and norm structure. Similar to operator system case, we define the unitalization of a possibly non-unital function system. Then we construct two possibly non-unital operator system structures on a given possibly non-unital function system, which are the analogues of minimal and maximal operator spaces on a normed space. These two structures have many interesting relations with the minimal and maximal operator system structures on a given function system.  相似文献   

3.
4.
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   

5.
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   

6.
7.
研究了两同型部件冷贮备可修系统.运用C_0半群理论,通过修复率均值的观念,对系统主算子的谱上界进行了估值,并得到该谱上界即为系统部件修复率均值的相反数.然后运用了共尾的概念及相关的理论,得到了系统主算子的谱上界与系统主算子产生的半群的增长界相等,从而得到其增长界也是修复率均值的相反数.  相似文献   

8.
In this paper we consider the nonselfadjoint (dissipative) Schrodinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint, the approach is based on the use of the maximal dissipative operator, and the spectral analysis of this operator is adequate for the boundary value problem. We construct a selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schrodinger equation. Theorems on the completeness of the system of eigenvectors and the associated vectors of the maximal dissipative operator and the Schrodinger boundary value problem are given.  相似文献   

9.
研究了有15个部件串并联工作的多状态口香糖生产可修复系统.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   

10.
研究了两同型部件温贮备可修系统.运用C_0半群理论,通过修复率均值的观念,对系统主算子的谱上界进行了估值,并得到该谱上界即为修复率均值的相反数.然后运用了共尾的概念及相关的理论,得到了系统主算子的谱上界与系统主算子产生的半群的增长界相等,从而得到其增长界也是修复率均值的相反数.  相似文献   

11.
In this paper we consider the nonselfadjoint (dissipative) Schrödinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint, the approach is based on the use of the maximal dissipative operator, and the spectral analysis of this operator is adequate for the boundary value problem. We construct a selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schrödinger equation. Theorems on the completeness of the system of eigenvectors and the associated vectors of the maximal dissipative operator and the Schrödinger boundary value problem are given.  相似文献   

12.
In this note, we develop the theory of characteristic function as an invariant for n-tuples of operators. The operator tuple has a certain contractivity condition put on it. This condition and the class of domains in Cn that we consider are intimately related. A typical example of such a domain is the open Euclidean unit ball. Given a polynomial P in C[z1,z2,…,zn] whose constant term is zero, all the coefficients are nonnegative and the coefficients of the linear terms are nonzero, one can naturally associate a Reinhardt domain with it, which we call the P-ball (Definition 1.1). Using the reproducing kernel Hilbert space HP(C) associated with this Reinhardt domain in Cn, S. Pott constructed the dilation for a polynomially contractive commuting tuple (Definition 1.2) [S. Pott, Standard models under polynomial positivity conditions, J. Operator Theory 41 (1999) 365-389. MR 2000j:47019]. Given any polynomially contractive commuting tuple T we define its characteristic function θT which is a multiplier. We construct a functional model using the characteristic function. Exploiting the model, we show that the characteristic function is a complete unitary invariant when the tuple is pure. The characteristic function gives newer and simpler proofs of a couple of known results: one of them is the invariance of the curvature invariant and the other is a Beurling theorem for the canonical operator tuple on HP(C). It is natural to study the boundary behaviour of θT in the case when the domain is the Euclidean unit ball. We do that and here essential differences with the single operator situation are brought out.  相似文献   

13.
给出了分数阶灰色累减生成算子的详细推导过程,并证明了分数阶灰色累减生成算子的不动点定理、信息优先原理、交换律与指数律,为分数阶灰色预测模型提供了理论基础.算例验证了分数阶灰色累减生成算子的特征,在灰色预测模型GM(1,1)中的应用证明了分数阶灰色累减生成算子的有效性.  相似文献   

14.
In this paper we consider the nonselfadjoint (dissipative) Schr(o)dinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint, the approach is based on the use of the maximal dissipative operator,and the spectral analysis of this operator is adequate for the boundary value problem. We construct a selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schr(o)dinger equation. Theorems on the completeness of the system of eigenvectors and the associated vectors of the maximal dissipative operator and the Schr(o)dinger boundary value problem are given.  相似文献   

15.
The main purpose of this paper is to study the validity of theHausdorff–Young inequality for vector-valued functionsdefined on a non-commutative compact group. As we explain inthe introduction, the natural context for this research is thatof operator spaces. This leads us to formulate a whole new theoryof Fourier type and cotype for the category of operator spaces.The present paper is the first step in this program, where thebasic theory is presented, the main examples are analyzed andsome important questions are posed. 2000 Mathematics SubjectClassification 43A77, 46L07.  相似文献   

16.
用链式模型讨论圣文南原理   总被引:1,自引:0,他引:1  
用泛函分析的双空间理论为计算力学构造卫一个严密的背景理论,以此在链式模型上讨论圣南原理,同时将传统的连分数扩展为算子连分式作为链式模型的本征关系式,平衡力系的影响在链式模型上由近及远扩衰减受算子边分式的收敛性的控制,所以南原理的合理成分体现为算子连分式的收敛性,发散的算子连分式对应着平衡力系的明显非零的影响可以传达到无穷远的场合,所以“圣南原理”并不是普遍成立的原理。  相似文献   

17.
In this paper, we present a recently developed mathematical model for a short double-wall carbon nanotube. The model is governed by a system of two coupled hyperbolic equations and is reduced to an evolution equation. This equation defines a dissipative semi-group. We show that the semi-group generator is an unbounded nonselfadjoint operator with compact resolvent. Moreover, this operator is a relatively compact perturbation of a certain selfadjoint operator.  相似文献   

18.
两同型部件温贮备可修系统解的指数渐近稳定性   总被引:1,自引:0,他引:1  
运用强连续半群理论研究两同型部件温贮备可修系统解的指数渐近性质,首先证明系统所生成的C0半群T(t)是拟紧的.其次证明0是对应于系统的主算子及其共轭算子的几何重数和代数重数为1的特征值,推出在右半平面和虚轴上除0以外其他所有点都属于该算子的豫解集,由此推出该系统的时间依赖解当时刻趋向于无穷时强收敛于系统的稳态解.  相似文献   

19.
A new approach for symbolically solving linear boundary value problems is presented. Rather than using general-purpose tools for obtaining parametrized solutions of the underlying ODE and fitting them against the specified boundary conditions (which may be quite expensive), the problem is interpreted as an operator inversion problem in a suitable Banach space setting. Using the concept of the oblique Moore—Penrose inverse, it is possible to transform the inversion problem into a system of operator equations that can be attacked by virtue of non-commutative Gröbner bases. The resulting operator solution can be represented as an integral operator having the classical Green’s function as its kernel. Although, at this stage of research, we cannot yet give an algorithmic formulation of the method and its domain of admissible inputs, we do believe that it has promising perspectives of automation and generalization; some of these perspectives are discussed.  相似文献   

20.
There exists a deep relationship between the nonexplosion conditions for Markov evolution in classical and quantum probability theories. Both of these conditions are equivalent to the preservation of the unit operator (total probability) by a minimal Markov semigroup. In this work, we study the Heisenberg evolution describing an interaction between the chain ofN two-level atoms andn-mode external Bose field, which was considered recently by J. Alli and J. Sewell. The unbounded generator of the Markov evolution of observables acts in the von Neumann algebra. For the generator of a Markov semigroup, we prove a nonexplosion condition, which is the operator analog of a similar condition suggested by R. Z. Khas’minski and later by T. Taniguchi for classical stochastic processes. For the operator algebra situation, this condition ensures the uniqueness and conservativity of the quantum dynamical semigroup describing the Markov evolution of a quantum system. In the regular case, the nonexplosion condition establishes a one-to-one relation between the formal generator and the infinitesimal operator of the Markov semigroup. Translated fromMatematicheskie Zemetki, Vol. 67, No. 5, pp. 788–796, May, 2000.  相似文献   

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