共查询到20条相似文献,搜索用时 15 毫秒
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Self-adjoint quadratic operator pencilsL()=
2
A + B + C with a noninvertible leading operatorA are considered. In particular, a characterization of the spectral points of positive and of negative type ofL is given, and their behavior under a compact perturbation is studied. These results are applied to a pencil arising in magnetohydrodynamics. 相似文献
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I. V. Kurbatova 《Mathematical Notes》2009,86(3-4):361-367
A direct relationship between the theory of pseudoresolvents and the spectral theory of linear operator pencils is established. 相似文献
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Functional Analysis and Its Applications - 相似文献
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G. A. Isaev 《Mathematical Notes》1973,13(4):333-338
Sufficient conditions are found for the linear factorization of polynomial operator pencils of arbitrary order in a Banach space. This factorization is generated by the solution of an appropriate operator equation.Translated from Matematicheskie Zametki, Vol. 13, No. 4, pp. 551–559, April, 1973.The author wishes to express his thanks to A. G. Kostyuchenko for the formulation of the problem. 相似文献
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M. Hasanov 《Mathematische Nachrichten》2006,279(8):843-853
The paper introduces a new class of two parameter non‐overdamped operator pencils arising from evolution equations. We investigate spectral properties, including variational principles for “interior” points of the spectrum. Examples leading to pencils of the new class are given. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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In this paper operator pencilsA(x, D, ) are studied which act on a manifold with boundary and satisfy the condition of N-ellipticity with parameter, a generalization of the notion of ellipticity with parameter as introduced by Agmon and Agranovich-Vishik. Sobolev spaces corresponding to the Newton polygon are defined and investigated; in particular it is possible to describe their trace spaces. With respect to these spaces, an a priori estimate is proved for the Dirichlet boundary value problem connected with an N-elliptic pencil.Supported in part by the Deutsche Forschungsgemeinschaft and by Russian Foundation of Fundamental Research, Grant 00-01-00387. 相似文献
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Nobukazu Otsuki Sintaro Suzuki 《Proceedings of the American Mathematical Society》2006,134(12):3637-3644
We discovered a certain class of linear Hamiltonian maps which are defined by explicit time dependent Hamiltonian functions. Our method is the analogy of Moser's construction in 1986, although it is not so difficult, but we think the results are new.
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In this paper parameter-dependent partial differential operators are investigated which satisfy the condition of N-ellipticity with parameter, an ellipticity condition formulated with the use of the Newton polygon. For boundary value problems with general boundary operators we define N-ellipticity including an analogue of the Shapiro-Lopatinskii condition. It is show that the boundary value problem is N-elliptic if and only if an a priori estimate with respect to certain parameter-dependent norms holds. These results are closely connected with singular perturbation theory and lead to uniform estimates, for problems of Vishik-Lyusternik type containing a small parameter.Supported in part by the Deutsche Forschungsgemeinschaft and by Russian Foundation of Fundamental Research, Grant 00-01-00387. 相似文献
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J. H. E. Cohn 《Proceedings of the American Mathematical Society》2002,130(5):1275-1277
Theorem. Let 2$"> denote an integer, the square-free part of and the class number of the field . Then except for the case , divides .
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Ren-Cang Li. 《Mathematics of Computation》2003,72(242):715-728
This paper continues earlier studies by Bhatia and Li on eigenvalue perturbation theory for diagonalizable matrix pencils having real spectra. A unifying framework for creating crucial perturbation equations is developed. With the help of a recent result on generalized commutators involving unitary matrices, new and much sharper bounds are obtained.
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V. A. Zolotarev 《Functional Analysis and Its Applications》2012,46(4):308-312
In this paper we describe the class of commuting pairs of bounded linear operators {A 1,A 2} acting on a Hilbert space H which are unitarily equivalent to the system of integrations over independent variables $$ (\tilde A_1 f)(x,y) = i\int_x^a {f(t,y)} dt, (\tilde A_2 f)(x,y) = i\int_y^b {f(x,s)} ds $$ in $ L_{\Omega _L }^2 $ , where ?? L is the compact set in ? + 2 bounded by the lines x = a and y = b and by a decreasing smooth curve L = {((x, p(x)): p(x) ?? C [0,a] 1 , p(0) = b, p(a) = 0}. 相似文献
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V. A. Kozlov 《Journal of Mathematical Sciences》1986,35(1):2180-2193
One gives a qualified remainder estimate in the asymptotic formulas of the distribution functions of the positive and negative spectra of a linear pencil of differential operators, where the lowest operator is not assumed to be elliptic.Translated from Problemy Maternaticheskogo Analiza, No. 9, pp. 34–56, 1984. 相似文献
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M. Yu. Kokurin 《Siberian Mathematical Journal》1995,36(4):727-734
The research was financially supported by the International Science Foundation (Grant NMW000). 相似文献
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B. M. Podlevskii 《Journal of Mathematical Sciences》1996,79(6):1397-1401
We study the generalized eigenvalue problem for a uniformly hyperbolic or totally hyperbolic polynomial operator pencil of
arbitrary order. In the context of the variational approach to the problem of determining the eigenvalues of such pencils
we propose and justify a recursive algorithm for finding an eigenpair. To accelerate the convergence we propose using the
Rayleigh-Ritz procedure. We give data from a numerical implementation of the algorithm.
Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 37, 1994, pp. 24–28. 相似文献