共查询到20条相似文献,搜索用时 15 毫秒
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Cornelis V. M. van der Mee André C. M. Ran L. Rodman 《Integral Equations and Operator Theory》1998,30(4):432-451
We describe in terms of canonical forms various classes of plus matrices in real and complex finite dimensional spaces with indefinite scalar product and study their topological structures (such as closure and interior).Dedicated to M.G. Kreîn, one of the founding fathers of the theory of plus-operators.The work of this author was performed under the auspices of C.N.R.-G.N.F.M. and partially supported by the research project, Nonlinear problems in analysis and its physical, chemical and biological applications: Analytical, modelling and computational aspects, of the Italian Ministry of Higher Education and Research (M.U.R.S.T.)The work of this author partially supported by the NSF grant DMS 9500924.The work of all authors is partially supported by the NATO grant CGR 960700. 相似文献
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Allan M Krall 《Journal of Mathematical Analysis and Applications》1979,70(1):267-279
When ?j ? 1 < α < ?j, where j is a positive integer, the Laguerre polynomials {Ln(α)}n = 0∞ form a complete orthogonal set in a nondegenerate inner product space H which is defined by employing an appropriate regularized linear functional on H(j)[[0, ∞); xα + je?x]. Expansions in terms of these Laguerre polynomials are exhibited. The Laguerre differential operator is shown to be self-adjoint with real, discrete, integer eigenvalues. Its spectral resolution and resolvent are exhibited and discussed. 相似文献
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Ivana M. Radojević 《Czechoslovak Mathematical Journal》2014,64(1):91-103
In this paper we study J-EP matrices, as a generalization of EP-matrices in indefinite inner product spaces, with respect to indefinite matrix product. We give some properties concerning EP and J-EP matrices and find connection between them. Also, we present some results for reverse order law for Moore-Penrose inverse in indefinite setting. Finally, we deal with the star partial ordering and improve some results given in the “EP matrices in indefinite inner product spaces” (2012), by relaxing some conditions. 相似文献
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Xiaonan Wu Gene H. Golub José A. Cuminato Jin Yun Yuan 《BIT Numerical Mathematics》2008,48(1):139-162
As an application of the symmetric-triangular (ST) decomposition given by Golub and Yuan (2001) and Strang (2003), three block
ST preconditioners are discussed here for saddle point problems. All three preconditioners transform saddle point problems
into a symmetric and positive definite system. The condition number of the three symmetric and positive definite systems are
estimated. Therefore, numerical methods for symmetric and positive definite systems can be applied to solve saddle point problems
indirectly. A numerical example for the symmetric indefinite system from the finite element approximation to the Stokes equation
is given. Finally, some comments are given as well.
AMS subject classification (2000) 65F10 相似文献
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V. A. Derkach 《Mathematical Notes》1998,63(4):449-459
The Laguerre-Sonin polynomialsL
n
()
are orthogonal in linear spaces with indefinite inner product if<–1. We construct the completion () of this space and describe self-adjoint extensions of the Laguerre operatorl(y)=xy+(1+–x)y,<–1, in the space (). In particular, we write out the self-adjoint extension of the Laguerre operator whose eigenfunctions coincide with the Laguerre-Sonin polynomials and form an orthogonal basis in ().Translated fromMatematicheskie Zametki, Vol. 63, No. 4, pp. 509–521, April, 1998.This research was partially supported by the INTAS foundation under grant No. 93-02449. 相似文献
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William J. Rolli 《Journal of Mathematical Analysis and Applications》2006,321(1):388-395
In this paper, we use the characterization of frames, introduced in [W. Rolli, A characterization of frames for finite dimensional Hilbert spaces, preprint], to construct frames for finite dimensional Hilbert spaces. Furthermore this approach allows for the construction of frames with prescribed properties. 相似文献
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The paper contains a survey of papers reviewed in Ref. Zh. Matematika from 1953–1978 on the theory of linear operators in (mainly Hibert) spaces with indefinite metric and their applications to various domains of mathematics and mechanics. As a preliminary, the needed results on the geometry of spaces with indefinite metric are described.Translated from Itogi Nauki i Tekhniki, Matematicheskii Analiz, Vol. 17, pp. 113–206, 1979. 相似文献
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Allan M Krall 《Journal of Mathematical Analysis and Applications》1982,85(2):406-408
It is shown that, when α < ?1, the Laguerre operator ly = xy′' + (1 + α ? x)y′ requires more than one boundary condition at x = 0 in order to be self-adjoint. The more negative α, the more boundary conditions required. 相似文献
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《Optimization》2012,61(4):895-907
In this paper, we introduce and study a new class of differential quasi-variational inequalities in finite dimensional Euclidean spaces. First, we prove existence theorems for Carathéodory weak solutions of the differential quasi-variational inequalities under various conditions. Furthermore, we establish a convergence result on Euler time-dependent procedure for solving the initial-value differential set-valued variational inequalities. 相似文献
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Michael H. Moore 《Linear algebra and its applications》1974,8(3):213-224
Let m be an integer ? 2. The effect of crowding m unit vectors x1,…,xm into the real Euclidean space Rn of n dimensions is investigated. In particular, several upper bounds for the quantity mini≠j∥xi ? xj∥ are obtained. These are simpler than any previously known and, at least in some cases, almost as sharp. The results have application to the so-called maximum-dispersal (or “misanthrope”) problem, an open problem recently popularized by Klee. 相似文献
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V. V. Sergeichuk 《Ukrainian Mathematical Journal》1990,42(4):487-491
Up to the classification of Hermitian forms a classification has been given of triplesP=(VF; U1, U2), consisting of a finite dimensional vector space V over a field of characteristic 2 with a symmetric, or a skew-symmetric, or Hermitian form F and two subspaces U1, U2. Two triplesP andP are identified with each other if there exists an isometry Vf Vf such that (Ui)=Ui, i=1, 2.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 4, pp. 549–554, April, 1990. 相似文献
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Reza Saadati S. Mansour Vaezpour 《Journal of Mathematical Analysis and Applications》2008,346(2):446-450
In this paper, we consider strongly bounded linear operators on a finite dimensional probabilistic normed space and define the topological isomorphism between probabilistic normed spaces. Then we prove that every finite dimensional probabilistic normed space which is a topological vector space is complete. 相似文献
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Xue-song Li Nan-jing Huang Donal O’Regan 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(9-10):3875-3886
In this paper, we introduce and study a class of differential mixed variational inequalities in finite dimensional Euclidean spaces. Under various conditions, we obtain linear growth and bounded linear growth of the solution set for the mixed variational inequalities. Moreover, we present some conclusions which enrich the literature on the mixed variational inequalities and generalize the corresponding results of [4]. In particular we prove existence theorems for weak solutions of a differential mixed variational inequality in the weak sense of Carathéodory by using a result on differential inclusions involving an upper semicontinuous set-valued map with closed convex values. Also by employing the results from differential inclusions we establish a convergence result on Euler time-dependent procedure for solving initial-value differential mixed variational inequalities. 相似文献
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In this paper, we prove that in a finite dimensional probabilistic normed space, every two probabilistic norms are equivalent
and we study the notion ofD-compactness and D-boundedness in probabilistic normed spaces. 相似文献