共查询到20条相似文献,搜索用时 31 毫秒
1.
M. S. Bichegkuev 《Russian Mathematics (Iz VUZ)》2008,52(8):12-19
We establish the necessary and sufficient conditions for the uniqueness of a solution to a difference inclusion in the space of bilateral vector sequences. The proof of the main result is based on the spectral theory of linear relations (multivalued linear operators). 相似文献
2.
Teresa Álvarez 《Mathematical Methods in the Applied Sciences》2015,38(9):1838-1846
A classical formula for the gap between two densely defined closed operators in a Hilbert space is extended to the case of linear relations. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
3.
We consider the relationship between the spectral properties of linear relations (multivalued linear operators) on real Banach spaces and their complexifications. 相似文献
4.
本文利用有限差分算子和组合恒等式为工具,给出了线性递归关系中序列{an}求解的新方法,与原来特征多项式法比较,它有两点好处;其一是简化了计算的过程;其二是避免了建立递归关系时复杂的推导。 相似文献
5.
This paper focuses on boundedness and closedness of linear relations, which include both single-valued and multi-valued linear operators. A new (single-valued) linear operator induced by a linear relation is introduced, and its relationships with other two important induced linear operators are established. Several characterizations for closedness, closability, bundedness, relative boundedness and boundedness from below (above) of linear relations are given in terms of their induced linear operators. In particular, the closed graph theorem for linear relations in Banach spaces is completed, and stability of closedness of linear relations under bounded and relatively bounded perturbations is studied. The results obtained in the present paper generalize the corresponding results for single-valued linear operators to multi-valued linear operators, and some improve or relax certain assumptions of the related existing results. 相似文献
6.
《Optimization》2012,61(4):487-504
Maximally monotone operators play a key role in modern optimization and variational analysis. Two useful subclasses are rectangular (also known as star monotone) and paramonotone operators, which were introduced by Brezis and Haraux, and by Censor, Iusem and Zenios, respectively. The former class has a useful range of properties while the latter class is of importance for interior point methods and duality theory. Both notions are automatic for subdifferential operators and known to coincide for certain matrices; however, more precise relationships between rectangularity and paramonotonicity were not known. Our aim is to provide new results and examples concerning these notions. It is shown that rectangularity and paramonotonicity are actually independent. Moreover, for linear relations, rectangularity implies paramonotonicity but the converse implication requires additional assumptions. We also consider continuous linear monotone operators, and we point out that in the Hilbert space both notions are automatic for certain displacement mappings. 相似文献
7.
Guixin Xu 《Linear and Multilinear Algebra》2018,66(12):2438-2467
This paper is concerned with the stability of essential spectra of self-adjoint relations under relatively compact perturbation in Hilbert spaces. Relationships between relative boundedness and relative compactness of linear relations are established, and some necessary and sufficient conditions of relative compactness and relative boundedness of linear relations are given. It is shown that the essential spectra of self-adjoint relations are invariant under either relatively compact perturbation or a more general perturbation. The results obtained in the present paper generalize the corresponding results for operators to relations, and some of which weaken certain assumptions of the related existing results. 相似文献
8.
范亚静 《应用泛函分析学报》2012,14(3):265-273
将单值算子的Fredholm对的概念推广到多值线性算子的范畴上,讨论了Fredholm多值线性算子对的一些初等性质,在适当的条件下,获得了正则的Fredholm多值线性算子对的与正则Fredholm算子对的相平行的一些结果. 相似文献
9.
Yahya Mezroui 《Transactions of the American Mathematical Society》2000,352(6):2789-2800
Let denote the set of all closed linear relations on a Hilbert space (which contains all closed linear operators on ). In this paper, for every we define and study two associated linear operators on , and , which play an important role in the study of linear relations. These operators satisfy conditions quite analogous to trigonometric identities (whence their names) and appear, in particular, in the formula that gives the orthogonal projection on the graph of , a formula first established for linear operators by M. H. Stone and extended to linear relations by H. De Snoo. We prove here a slightly modified version of the De Snoo formula. Several other applications of the and operators to operator theory will be given in a forthcoming paper.
10.
Teresa Álvarez Aymen Ammar Aref Jeribi 《Mathematical Methods in the Applied Sciences》2014,37(5):620-644
In this paper, we investigate a detailed treatment of some subsets of essential spectra of a closed multivalued linear operator. On the following, we will establish some results on perturbation theory of 2 × 2 matrix of multivalued linear operators. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
11.
Guojing Ren 《Indagationes Mathematicae》2018,29(2):657-670
This paper is concerned with the stability of linear relations in Banach and Hilbert spaces. Several important results about the stability of closedness and the stability of indices of operators in Banach spaces are extended to the linear relations in Banach spaces. Moreover, the stability of deficiency indices of dissipative linear relations in Hilbert spaces is studied. As an important application, we discuss the stability of deficiency indices of dissipative linear relations generated by second-order difference expressions. 相似文献
12.
A generalized linear differential equation in a Banach space is studied. The construction of a phase space and solutions with the help of the spectral theory of linear operators, ergodic theorems, and degenerate semigroups of linear operators is carried out. 相似文献
13.
In this paper we investigate the stability of the index, the nullity and the deficiency of normally solvable linear relations in paracomplete spaces under perturbation by strictly singular and T-strictly singular linear relations. This study led us to generalize some well-known results for operators and extend some results of small perturbation of normally solvable linear relations given by T. Alvarez (2012) [3]. 相似文献
14.
《Expositiones Mathematicae》2020,38(1):60-90
This work is devoted to dissipative extension theory for dissipative linear relations. We give a self-consistent theory of extensions by generalizing the theory on symmetric extensions of symmetric operators. Several results on the properties of dissipative relations are proven. Finally, we deal with the spectral properties of dissipative extensions of dissipative relations and provide results concerning particular realizations of this general setting. 相似文献
15.
Seppo Hassi Adrian Sandovici Henk de Snoo Henrik Winkler 《Acta Mathematica Hungarica》2006,111(1-2):81-105
Summary The sum of two unbounded nonnegative selfadjoint operators is a nonnegative operator which is not necessarily densely defined.
In general its selfadjoint extensions exist in the sense of linear relations (multivalued operators). One of its nonnegative
selfadjoint extensions is constructed via the form sum associated with A and B. Its relations to the Friedrichs and Krein--von Neumann extensions of A+Bare investigated. For this purpose, the one-to-one correspondence between densely defined closed semibounded forms and semibounded
selfadjoint operators is extended to the case of nondensely defined semibounded forms by replacing semibounded selfadjoint
operators by semibounded selfadjoint relations. In particular, the inequality between two closed nonnegative forms is shown
to be equivalent to a similar inequality between the corresponding nonnegative selfadjoint relations.</o:p> 相似文献
16.
We study distribution semigroups with a singularity at zero and their generators, and establish a relationship between this semigroup and a degenerate semigroup of linear operators on the open right half-line. The study makes an intensive use of spectral theory of linear relations. Applications to the existence problem for bounded solutions of linear differential inclusions are obtained. 相似文献
17.
18.
Vakeel A. Khan Kamal M. A. S. Alshlool Sameera A. A. Abdullah 《Numerical Functional Analysis & Optimization》2013,34(12):1278-1290
AbstractThe notation of I–convergence was introduced and studied by Kostyrko, Macaj, Salat, and Wilczynski. Recently, the concept of I–convergent for a sequence of bounded linear operators has been studied by Khan and Shafiq. This has motivated us to introduce and study some new spaces of double sequences of bounded linear operators and their basic topological and algebraic properties of these spaces. And we study some of their basic topological and algebraic properties of these spaces. We prove some inclusion relations on these spaces. 相似文献
19.
In this paper, extensions of several relations linking differences of bivariate discrete orthogonal polynomials and polynomials themselves are given, by using an appropriate vector–matrix notation. Three-term recurrence relations are presented for the partial differences of the monic polynomial solutions of admissible second order partial difference equation of hypergeometric type. Structure relations, difference representations as well as lowering and raising operators are obtained. Finally, expressions for all matrix coefficients appearing in these finite-type relations are explicitly presented for a finite set of Hahn and Kravchuk orthogonal polynomials. 相似文献
20.
Yuji Yoshida Masami Yasuda Jun-ichi Nakagami Masami Kurano 《Fuzzy Sets and Systems》1993,60(3):283-294
In this paper we develop a potential theory of fuzzy relations on the positive orthant in a Euclidean space. By introducing a linear structure for fuzzy relations, the existence of a potential and its characterization by fuzzy relational equation are derived under the assumption of contraction and compactness. In the one-dimensional unimodal case, a potential is given explicity. Also, a numerical example is shown to illustrate our approaches. 相似文献