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Several results are presented that relate the stability properties of a perturbed linear nonstationary system ?(t) = (A(t) + B(t)) x(t) to those of an unperturbed linear system ?(t) = A(t) x(t). Similarly, the stability properties of the discrete system xk + 1 = (Ak + Bk) xk are related to those of xk + 1 = Akxk.  相似文献   

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We describe the bifurcation hypersurfaces for periodic solutions of a singularly perturbed linear differential difference equation in the space of the coefficients of the equation. For low dimension we show that the locus of stability of that equation approaches the locus of stability of a limit difference equation.  相似文献   

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We show that a necessary condition for stable perturbations in linear and convex programming is valid on an arbitrary region of stability. Using point-to-set mappings, two new regions of stability are identified.Contribution of this author is part of his M.Sc. thesis in Applied Mathematics at McGill University.  相似文献   

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In this paper, an alternate approach to the method of asymptotic expansions for the study of a singularly perturbed, linear system with multiparameters and multi-time scales, is developed. The method consists of developing a linear, nonsingular transformation that enables to decouple the original system completely. This process of diagonalization thus provides a very simple and suitable tool to investigate (i) the stability analysis and (ii) approximations of solutions of original system in terms of the overall reduced system and the corresponding boundary layer systems.  相似文献   

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Siberian Mathematical Journal -  相似文献   

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In this paper we find necessary and sufficient conditions for the existence of a Laurent series expansion with a finite order pole at the origin for the inverse of a linearly perturbed bounded linear operator mapping one Banach space to another. In particular we show that the inversion defines linear projections that separate the Banach spaces into corresponding complementary subspaces. We present two pertinent applications.  相似文献   

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Spectral properties of the sum of a linear span of projections and a compact nonnegative operator are considered. In particular, we prove partial completeness results for certain parts of the system of eigenfunctions. The main tool is a transformation the original spectral problem to that of a monic weakly hyperbolic pencil.  相似文献   

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In this work we give sufficient conditions on the semigroup (T 0 (t)) tgeq0 , generated by the part of a Hille—Yosida operator in the closure of its domain, in order that certain perturbations preserve some regularity properties of (T 0 (t)) tgeq0 , like the norm continuity, compactness and differentiability. An application of our abstract results to retarded differential equations is given.  相似文献   

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Let \({\mathcal {A}}\) and \({\mathcal {B}}\) be commutative Banach algebras, and let \(T:{\mathcal {B}} \rightarrow {\mathcal {A}}\) be an algebra homomorphism with \({\Vert T\Vert }\le 1\). Then T induces a Banach algebra product \(\times _T\) perturbing the coordinatewise product on the Cartesian product space \({\mathcal {A}} \times {\mathcal {B}}\). We show that the spectral properties like spectral extension property, unique uniform norm property, regularity, weak regularity as well as Ditkin’s condition are stable with respect to this product.  相似文献   

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In the present paper we introduce a generalization of positive linear operators and obtain its Korovkin type approximation properties. The rates of convergence of this generalization is also obtained by means of modulus of continuity and Lipschitz type maximal functions. The second purpose of this paper is to obtain weighted approximation properties for the generalization of positive linear operators defined in this paper. Also we obtain a differential equation so that the second moment of our operators is a particular solution of it. Lastly, some Voronovskaja type asymptotic formulas are obtained for Meyer-König and Zeller type and Bleimann, Butzer and Hahn type operators.  相似文献   

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The paper deals with the spectral and oscillatory properties of a linear operator pencilA ? λB, where the coefficient A corresponds to the differential expression (py″)″ and the coefficient B corresponds to the differential expression ?y″ + cry. In particular, it is shown that all negative eigenvalues of the pencil are simple and, under some additional conditions, the number of zeros of the corresponding eigenfunctions is related to the serial number of the corresponding eigenvalue.  相似文献   

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In the framework of [5] we prove regularity of invariant measures for a class of Ornstein-Uhlenbeck operators perturbed by a drift which is not necessarily bounded or Lipschitz continuous. Regularity here means that is absolutely continuous with respect to the Gaussian invariant measure of the unperturbed operator with the square root of the Radon-Nikodym density in the corresponding Sobolev space of order 1.Partially supported by the International Science Foundation (Grant M 38000), the Russian Foundation of Fundamental Research (Grant 94-01-01556), and EC-Science Project SC1*CT92-0784.Partially supported by the Italian National Project MURST Problemi nonlineari nell'AnalisiPartially supported by the DFG(SFB-256-Bonn, SFB-343-Bielefeld) and EC-Science Project SC1*CT92-0784.  相似文献   

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The spectral properties of a bunchA–B, D(A)D(B), of linear closed densely defined operators in Banach space are considered. Our main result is a theorem to the effect that the spectrum of the bunch can be expanded with respect to a pair of direct sums; the theorem generalizes the celebrated theorem of Riesz concerning the expansion of the spectrum of an operator.Translated from Matematicheskie Zametki, Vol. 22, No. 6, pp. 847–857, December, 1977.  相似文献   

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