共查询到20条相似文献,搜索用时 46 毫秒
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We prove that a first-order linear differential operator G with unbounded operator coefficients is Fredholm on spaces of functions on with values in a reflexive Banach space if and only if the corresponding strongly continuous evolution family has exponential dichotomies on both and and a pair of the ranges of the dichotomy projections is Fredholm, and that the Fredholm index of G is equal to the Fredholm index of the pair. The operator G is the generator of the evolution semigroup associated with the evolution family. In the case when the evolution family is the propagator of a well-posed differential equation u′(t)=A(t)u(t) with, generally, unbounded operators , the operator G is a closure of the operator . Thus, this paper provides a complete infinite-dimensional generalization of well-known finite-dimensional results by Palmer, and by Ben-Artzi and Gohberg. 相似文献
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Quadratic minimisation problems in statistics 总被引:1,自引:0,他引:1
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Michael Solomyak 《Journal of Approximation Theory》2003,121(2):199-219
Some results on the approximation of functions from the Sobolev spaces on metric graphs by step functions are obtained. In particular, we show that the approximation numbers an of the embedding operator of the Sobolev space on a graph G of finite length |G| into the space , where μ is an arbitrary finite Borel measure on G, satisfy the inequality
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Ngoc Gioan Jean Pagnon 《Indagationes Mathematicae》2004,15(1):101-114
In the article [Spa1], N. Spaltenstein has established a bijection between the irreducible components of χ, the space of full flags fixed by a nilpotent element χ ? M(n, k), where k is an algebraically closed field, and the standard tableaux associated to the Young diagram of χ. In this present work we determine, when χ is of hook type, for each irreducible component X of χ, the unique Schubert cell X of the full flag manifold = (V) (where V is vector space of dimension n over k), such that X ∩ X is a dense subspace in X. This result will allow us to optimize the computation of χ and when k = is the complex field, to see that the graph resolution of the partition (2, 1, …, 1) of n is related to the Dynkin diagram of sl(n, ). 相似文献
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Let γ be the Gauss measure on and the Ornstein-Uhlenbeck operator. For every p in [1,∞)?{2}, set , and consider the sector . The main results of this paper are the following. If p is in (1,∞)?{2}, and , i.e., if M is an Lp(γ)uniform spectral multiplier of in our terminology, and M is continuous on , then M extends to a bounded holomorphic function on the sector . Furthermore, if p=1 a spectral multiplier M, continuous on , satisfies the condition if and only if M extends to a bounded holomorphic function on the right half-plane, and its boundary value M(i·) on the imaginary axis is the Euclidean Fourier transform of a finite Borel measure on the real line. We prove similar results for uniform spectral multipliers of second order elliptic differential operators in divergence form on belonging to a wide class, which contains . From these results we deduce that operators in this class do not admit an H∞ functional calculus in sectors smaller than . 相似文献
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Applications of quadratic minimisation problems in statistics 总被引:1,自引:0,他引:1
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A min-max theorem for complex symmetric matrices 总被引:1,自引:0,他引:1
Jeffrey Danciger 《Linear algebra and its applications》2006,412(1):22-29
We optimize the form Re xtTx to obtain the singular values of a complex symmetric matrix T. We prove that for ,
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Preservers of spectral radius, numerical radius, or spectral norm of the sum on nonnegative matrices
Chi-Kwong Li 《Linear algebra and its applications》2009,430(7):1739-1398
Let be the set of entrywise nonnegative n×n matrices. Denote by r(A) the spectral radius (Perron root) of . Characterization is obtained for maps such that r(f(A)+f(B))=r(A+B) for all . In particular, it is shown that such a map has the form
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Let G be a connected Lie group with the Lie algebra . The action of Cameron-Martin space on the path space Pe(G) introduced by L. Gross (Illinois J. Math. 36 (1992) 447) is free. Using this fact, we define the H-distance on Pe(G), which enables us to establish a transportation cost inequality on Pe(G). This method will be generalized to the path space over the loop group , so that we obtain a transportation cost inequality for heat measures on . 相似文献