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Given two self-adjoint, positive, compact operators A,B on a separable Hilbert space, we show that there exists a self-adjoint, positive, compact operator C commuting with B such that
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L. A. Pastur 《Mathematical Notes》1989,46(3):712-716
Translated from Matematicheskie Zametki, Vol. 46, No. 3, pp. 50–57, September, 1989. 相似文献
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The singular values of a matrix and those of its exponential are related via multiplicative majorization. Matrices giving some equalities in the majorization are characterized. As an application, a scalar inequality for the exponential function is generalized to a matrix-valued inequality and the case of equality is examined. 相似文献
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In this paper, a generalization of a formula proposed by Van Loan [Computing integrals involving the matrix exponential, IEEE Trans. Automat. Control 23 (1978) 395–404] for the computation of multiple integrals of exponential matrices is introduced. In this way, the numerical evaluation of such integrals is reduced to the use of a conventional algorithm to compute matrix exponentials. The formula is applied for evaluating some kinds of integrals that frequently emerge in a number classical mathematical subjects in the framework of differential equations, numerical methods and control engineering applications. 相似文献
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SU ZHONGGEN 《高校应用数学学报(英文版)》1995,10(4):367-378
ONTHECENTRALLIMITTHEOREMINPRODUCTSPACESSUZHONGGENAbstract:SupposethatEandFareseparableBanachspaces,XandYareindependentsymmetr... 相似文献
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Motivated by models from stochastic population biology and statistical mechanics, we proved new inequalities of the form , where A and B are n × n complex matrices, 1<n<∞, and ? is a real-valued continuous function of the eigenvalues of its matrix argument. For example, if A is essentially nonnegative, B is diagonal real, and ? is the spectral radius, then (1) holds; if in addition A is irreducible and B has at least two different diagonal elements, then the inequality (1) is strict. The proof uses Kingman's theorem on the log-convexity of the spectral radius, Lie's product formula, and perturbation theory. We conclude with conjectures. 相似文献
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The double scaling limit of a new class of the multi-matrix models proposed in [1], which possess the W-symmetry at the discrete level, is investigated in details. These models are demonstrated to fall into the same universality class as the standard multi-matrix models. In particular, the transformation of the W-algebra at the discrete level into the continuum one of the paper [2] is proposed, the corresponding partition functions being compared. All calculations are demonstrated in full in the first non-trivial case of W(3)-constraints.This paper was supported in part by NSF grant PHY88-57200.Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 2, pp. 317–340, May, 1993. 相似文献
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《Operations Research Letters》2001,28(1):27-34
In this paper, we demonstrate a method for developing analytic Markovian traffic sources in which the correlation structure can be arbitrarily constructed leaving the marginals invariant. We construct a simple model based on empirical data sets and show the effects of changing the autocorrelation on the behavior of network traffic. 相似文献
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Let be a polynomial in the variables x1,…,xp with nonnegative real coefficients which sum to one, let A1,…,Ap be stochastic matrices, and let be the stochastic matrix which is obtained from ? by substituting the Kronecker product of An11,…,Anppfor each term Xn11·?·Xnpp. In this paper, we present necessary and sufficient conditions for the Cesàro limit of the sequence of the powers of to be equal to the Kronecker product of the Cesàro limits associated with each of A1,…,Ap. These conditions show that the equality of these two matrices depends only on the number of ergodic sets under and?or the cyclic structure of the ergodic sets under A1,…,Ap, respectively. As a special case of these results, we obtain necessary and sufficient conditions for the interchangeability of the Kronecker product and the Cesàro limit operator. 相似文献
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A. M. Sedletskii 《Journal of Mathematical Sciences》2008,155(1):170-182
Some conditions on sequences (λ n ) and (μ n ) to be nearby are given in order that the corresponding systems of complex exponentials (exp(iλ n t)) and (exp(iμ n t)) be simultaneously uniformly minimal in L p (−π, π), 1 ≤ p < ∞, and in C[−π, π]. __________ Translated from Sovremennaya Matematika. Fundamental'nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 25, Theory of Functions, 2007. 相似文献
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Fuchang Gao Lixing Han Kenneth Schilling 《Journal of Applied Mathematics and Computing》2012,39(1-2):89-96
We study the asymptotic rate of convergence of the sequence of iterated exponentials $\{ z_{1}=a, z_{n+1}=a^{z_{n}}, n \geq 1 \}$ . We show that z n converges at a linear rate if a is in the interior of the Baker-Rippon convergence region and at a sublinear rate if a is on its boundary. A precise characterization of the rate is explored when the sequence converges sublinearly. 相似文献
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The existence of limiting spectral distribution (LSD) of the product of two random matrices is proved. One of the random matrices is a sample covariance matrix and the other is an arbitrary Hermitian matrix. Specially, the density function of LSD of SnWn is established, where Sn is a sample covariance matrix and Wn is Wigner matrix. 相似文献
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Bounds for the pointwise or Schur product of two matrices are derived with respect to the spectral norm 6·6. For real symmetric and positive semidefinite matrices Q=(qij) one of them gives a bound of 6|Q6, |Q|=(|qij|). Two of these bounds are applied to obtain a mean value theorem for g: t→f(A(t)) where A(t) is a matrix depending on a parameter t and f is a function on the spectrum of A(t). 相似文献
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FOTIOS C PALIOGIANNIS 《Proceedings Mathematical Sciences》2013,123(1):27-31
We prove that, under sufficient conditions on the spectra, $$ e^Me^N\subseteq e^Ne^M\Rightarrow MN\subseteq NM , $$ where N is an unbounded normal operator and M is a bounded normal operator in the Hilbert space. 相似文献
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A new formulation for the limit matrix occurring in the cost functional of an optimal control problem on homogenization is
obtained. It is used to obtain an upper bound for this matrix (in the sense of positive definite matrices). 相似文献
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On the limit of the largest eigenvalue of the large dimensional sample covariance matrix 总被引:6,自引:0,他引:6
Summary In this paper the authors show that the largest eigenvalue of the sample covariance matrix tends to a limit under certain conditions when both the number of variables and the sample size tend to infinity. The above result is proved under the mild restriction that the fourth moment of the elements of the sample sums of squares and cross products (SP) matrix exist.Research sponsored by the Air Force Office of Scientific Research under Contract F49620-C-0008. The United States Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation hereonThe work of this author was done when he was working at the Center for Multivariate Analysis, University of Pittsburgh. 相似文献
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郑恒武 《纯粹数学与应用数学》1999,15(3):14-17
给出了拟正则半群的圈积嵌入.研究了幂等元集 E S 生成的子半群〈 E S〉上的矩阵同余可扩张为 S上的矩阵同余的条件. 特别地,如果〈 E S〉上的最小矩阵同余可扩张为 S上的矩阵同余,那么〈 E S〉上的每个矩阵同余可扩张为 S上的矩阵同余 相似文献