共查询到20条相似文献,搜索用时 31 毫秒
1.
M. I. Gil’ 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2011,62(1):87-97
We consider a second-order matrix ordinary regular differential nonselfadjoint operator with a damping term and selfadjoint boundary conditions. An estimate for the resolvent and bounds for the spectrum are established. An operator is said to be stable if its spectrum lies in the right half-plane. By the obtained bounds, stability and instability conditions are established. 相似文献
2.
M.I. Gil 《Positivity》2004,8(3):243-256
The paper deals with a class of nonselfadjoint operators in a separable Hilbert lattice. Conditions for the positive invertibility are derived. Moreover, upper and lower estimates for the inverse operator are established. In addition, bounds for the positive spectrum are suggested. Applications to integral operators, integro-differential operators and infinite matrices are discussed. 相似文献
3.
We prove a version of the Gohberg Lemma on compact Lie groups giving an estimate from below for the distance from a given operator to the set of compact operators. As a consequence, we obtain several results on bounds for the essential spectrum and a criterion for an operator to be compact. The conditions are given in terms of the matrix-valued symbols of operators. 相似文献
4.
M. I. Gil' 《Proceedings of the American Mathematical Society》2003,131(12):3737-3746
A linear operator in a separable Hilbert space is called a quasinormal one if it is a sum of a normal operator and a compact one. In the paper, bounds for the spectrum of quasinormal operators are established. In addition, the lower estimate for the spectral radius is derived. Under some restrictions, that estimate improves the well-known results. Applications to integral operators and matrices are discussed. Our results are new even in the finite-dimensional case.
5.
In a weighted Sobolev-type space, the well-posedness and unique solvability of a problem without initial conditions for a third-order operator-differential equation with an inverse parabolic principal part are established. The solvability conditions are expressed in terms of the operator coefficients of the equation. Additionally, the norms of the operators of intermediate derivatives closely related to the solvability conditions are estimated. The relation between the weight exponent and the lower boundary of the spectrum of the basic operator involved in the principal part of the equation is established. Note that the principal part of the equation has a multiple characteristic. 相似文献
6.
The semilocal convergence for a modified multi-point Jarratt method for solving non-linear equations in Banach spaces is established with the third-order Fréchet derivative of the operator under a general continuity condition. The recurrence relations are derived for the method, and from this, we prove an existence-uniqueness theorem, and give a priori error bounds. The R-order of the method is also analyzed with the third-order Fréchet derivative of the operator under different continuity conditions. Numerical application on non-linear integral equation of the mixed type is given to show our approach. 相似文献
7.
A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. An analytic function is identified which matches the discontinuity in the initial condition and also satisfies the homogenous parabolic differential equation associated with the problem. The difference between this analytical function and the solution of the parabolic problem is approximated numerically, using an upwind finite difference operator combined with an appropriate layer-adapted mesh. The numerical method is shown to be parameter-uniform. Numerical results are presented to illustrate the theoretical error bounds established in the paper.
相似文献8.
L. V. Dorodnitsyn 《Computational Mathematics and Modeling》2008,19(4):343-358
The properties of the spectra of discrete spatially one-dimensional problems of convection — diffusion type with constant
coefficients and nonstandard boundary conditions are examined in the framework of stability of explicit algorithms for time-dependent
problems of mathematical physics. An analytical method is proposed for finding isolated limit points of the operator spectrum.
Limit points are determined for the difference transport equation with different versions of nonreflecting boundary conditions
and for an approximation of the heat conduction equation on a grid with condensation near the boundary. Stability and other
properties of the spectrum are also established numerically.
__________
Translated from Prikladnaya Matematika i Informatika, No. 27, pp. 25–45, 2007. 相似文献
9.
M. I. Gil' 《Mathematische Nachrichten》2002,244(1):78-88
Hille–Tamarkin matrices are investigated.Invertibility conditions and estimates for the norm of the inverse matrices are established. In addition, bounds for the spectrum are suggested. In particular, new estimates for the spectral radius are derived. 相似文献
10.
Summary. A posteriori error estimators of residual type are derived for piecewise linear finite element approximations to elliptic
obstacle problems. An instrumental ingredient is a new interpolation operator which requires minimal regularity, exhibits
optimal approximation properties and preserves positivity. Both upper and lower bounds are proved and their optimality is
explored with several examples. Sharp a priori bounds for the a posteriori estimators are given, and extensions of the results
to double obstacle problems are briefly discussed.
Received June 19, 1998 / Published online December 6, 1999 相似文献
11.
In this paper, a class of singularly perturbed elliptic partial differential equations posed on a rectangular domain is studied.
The differential equation contains two singular perturbation parameters. The solutions of these singularly perturbed problems
are decomposed into a sum of regular, boundary layer and corner layer components. Parameter-explicit bounds on the derivatives
of each of these components are derived. A numerical algorithm based on an upwind finite difference operator and a tensor
product of piecewise-uniform Shishkin meshes is analysed. Parameter-uniform asymptotic error bounds for the numerical approximations
are established. 相似文献
12.
Sufficient conditions on the kernel and the grandizer that ensure the boundedness of integral operators with homogeneous kernels in grand Lebesgue spaces on ? n as well as an upper bound for their norms are obtained. For some classes of grandizers, necessary conditions and lower bounds for the norm of these operators are also obtained. In the case of a radial kernel, stronger estimates are established in terms of one-dimensional grand norms of spherical means of the function. A sufficient condition for the boundedness of the operator with homogeneous kernel in classical Lebesgue spaces with arbitrary radial weight is obtained. As an application, boundedness in grand spaces of the one-dimensional operator of fractional Riemann–Liouville integration and of a multidimensional Hilbert-type operator is studied. 相似文献
13.
M.I. Gil' 《Journal of Mathematical Analysis and Applications》2009,349(2):443-451
A compact operator in a separable Hilbert space is of infinite order if it does not belong to any Schatten-von Neumann ideal. In the paper, upper and lower bounds for the regularized determinants of infinite order operators are derived. By these bounds, perturbations results for the regularized determinants are established. 相似文献
14.
Sever S. Dragomir 《Linear algebra and its applications》2006,419(1):256-264
Some sharp bounds for the Euclidean operator radius of two bounded linear operators in Hilbert spaces are given. Their connection with Kittaneh’s recent results which provide sharp upper and lower bounds for the numerical radius of linear operators are also established. 相似文献
15.
Graeme W. Milton 《纯数学与应用数学通讯》1990,43(1):63-125
A general algebraic framework is developed for characterizing the set of possible effective tensors of composites. A transformation to the polarization-problem simplifies the derivation of the Hashin-Shtrikman variational principles and simplifies the calculation of the effective tensors of laminate materials. A general connection is established between two methods for bounding effective tensors of composites. The first method is based on the variational principles of Hashin and Shtrikman. The second method, due to Tartar, Murat, Lurie, and Cherkaev, uses translation operators or, equivalently, quadratic quasiconvex functions. A correspondence is established between these translation operators and bounding operators on the relevant non-local projection operator, T1. An important class of bounds, namely trace bounds on the effective tensors of two-component media, are given a geometrical interpretation: after a suitable fractional linear transformation of the tensor space each bound corresponds to a tangent plane to the set of possible tensors. A wide class of translation operators that generate these bounds is found. The extremal translation operators in this class incorporate projections onto spaces of antisymmetric tensors. These extremal translations generate attainable trace bounds even when the tensors of the two-components are not well ordered. In particular, they generate the bounds of Walpole on the effective bulk modulus. The variational principles of Gibiansky and Cherkaev for bounding complex effective tensors are reviewed and used to derive some rigorous bounds that generalize the bounds conjectured by Golden and Papanicolaou. An isomorphism is shown to underlie their variational principles. This isomorphism is used to obtain Dirichlet-type variational principles and bounds for the effective tensors of general non-selfadjoint problems. It is anticipated that these variational principles, which stem from the work of Gibiansky and Cherkaev, will have applications in many fields of science. 相似文献
16.
A Volterra type integral equation in a Hilbert space with an additional linear operator L and a spectral parameter depending
on time is considered. If the parameter does not belong to the spectrum of L unconditional solvability of the considered problem
is proved. In the case where the initial value of the parameter coincides with some isolated point of the spectrum of the
operator L sufficient conditions for solvability are established. The obtained results are applied to the partial integral
equations associated with a contact problem of the theory of elasticity. 相似文献
17.
M. Hasanov 《Acta Appl Math》2002,71(2):117-126
An approximation method, based on a theorem on approximating general operator-valued functions by piecewise-linear ones, is presented and analyzed. Using this method, variational characteristics of the spectrum of a class of operator functions are established. 相似文献
18.
侯学章 《应用泛函分析学报》2011,13(3):319-331
讨论了一类双臂三关节柔性梁系统的分析问题.首先,建立了一个与柔性梁的偏微分方程组及初值边值条件相应的希尔伯特空间中的一阶发展系统.接着讨论系统算子的谱性质和半群性质.最后借助系统算子的谱性质和半群性质提出并证明了柔性梁系统的指数稳定性. 相似文献
19.
A method for accelerating linear iterations in a Banach space is studied as a linear iterative method in an augmented space, and sufficient conditions for convergence are derived in the general case and in ordered Banach spaces. An acceleration of convergence takes place if an auxiliary functional is chosen sufficiently close to a dual eigenvector associated with a dominant simple eigenvalue of the iteration operator; in this case, the influence of this eigenvalue on the asymptotic rate of convergence is eliminated. Quantitative estimates and bounds on convergence are given. 相似文献
20.
I. S. Lobanov V. Yu. Lotoreichik I. Yu. Popov 《Theoretical and Mathematical Physics》2010,162(3):332-340
We consider the two-dimensional Schrödinger operator with a δ-potential supported by curve. For the cases of infinite and closed finite smooth curves, we obtain lower bounds on the spectrum of the considered operator that are expressed explicitly in terms of the interaction strength and a parameter characterizing the curve geometry. We estimate the bottom of the spectrum for a piecewise smooth curve using parameters characterizing the geometry of the separate pieces. As applications of the obtained results, we consider curves with a finite number of cusps and general “leaky” quantum graph as the support of the δ-potential. 相似文献