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The main topic of the paper is best constants in Markov-type inequalities between the norms of higher derivatives of polynomials and the norms of the polynomials themselves. The norm is the L2 norm with Laguerre weight. The leading term of the asymptotics of the constants is determined and tight bounds for the principal coefficient in this term, which is the operator norm of a Volterra operator, are given. For best constants in inequalities of the Wirtinger type, the limit is computed and an asymptotic formula for the error term is presented. 相似文献
3.
Jacob S. Christiansen Maxim Zinchenko 《Journal of Computational and Applied Mathematics》2009,233(3):652-662
We consider Jacobi matrices whose essential spectrum is a finite union of closed intervals. We focus on Szeg?’s theorem, Jost solutions, and Szeg? asymptotics for this situation. This announcement describes talks the authors gave at OPSFA 2007. 相似文献
4.
Harold Widom 《Integral Equations and Operator Theory》2007,57(1):133-151
The solution of a problem arising in integrable systems requires sharp asymptotics for the inverses and determinants of truncated
Wiener-Hopf operators, both in the regular case (where the non-truncated Wiener-Hopf operator is invertible) and in singular
cases. This paper treats two cases where the symbol of the Wiener-Hopf operator has Fisher-Hartwig singularities, one double
zero or two simple zeros. We find formulas for the inverse that hold uniformly throughout the underlying interval with very
small error, and formulas for the determinant with very small error. 相似文献
5.
We establish an asymptotic formula for determinants of truncated
Wiener-Hopf+Hankel operators with symbol equal to the exponential of a constant
times the characteristic function of an interval. This is done by reducing
it to the corresponding (known) asymptotics for truncated Toeplitz+Hankel
operators. The determinants in question arise in random matrix theory in determining
the limiting distribution for the number of eigenvalues in an interval
for a scaled Laguerre ensemble of positive Hermitian matrices. 相似文献
6.
A. Böttcher S. Grudsky E. A. Maksimenko J. Unterberger 《Integral Equations and Operator Theory》2009,63(2):165-180
The paper is concerned with Hermitian Toeplitz matrices generated by a class of unbounded symbols that emerge in several applications.
The main result gives the third order asymptotics of the extreme eigenvalues and the first order asymptotics of the extreme
eigenvectors of the matrices as their dimension increases to infinity.
This work was partially supported by CONACYT projects 60160 and 80504, Mexico. 相似文献
7.
We consider large finite Toeplitz matrices with symbols of the form (1– cos )p f() where p is a natural number and f is a sufficiently smooth positive function. By employing techniques based on the use of predictor polynomials, we derive exact and asymptotic formulas for the entries of the inverses of these matrices. We show in particular that asymptotically the inverse matrix mimics the Green kernel of a boundary value problem for the differential operator
Submitted: June 20, 2003 相似文献
8.
Jon Johnsen 《Integral Equations and Operator Theory》2000,36(3):288-324
A study is made of a recent integral identity of B. Helffer and J. Sjöstrand, which for a not yet fully determined class of probability measures yields a formula for the covariance of two functions (of a stochastic variable); in comparison with the Brascamp-Lieb inequality, this formula is a more flexible and in some contexts stronger means for the analysis of correlation asymptotics in statistical mechanics. Using a fine version of the Closed Range Theorem, the identity's validity is shown to be equivalent to some explicitly given spectral properties of Witten-Laplacians on Euclidean space, and the formula is moreover deduced from the obtained abstract expression for the range projection. As a corollary, a generalised version of Brascamp-Lieb's inequality is obtained. For a certain class of measures occuring in statistical mechanics, explicit criteria for the Witten-Laplacians are found from the Persson-Agmon formula, from compactness of embeddings and from the Weyl calculus, which give results for closed range, strict positivity, essential self-adjointness and domain characterisations.Supported by TMR grant FMRX-CT960001 of the European Commision, PDE and QM at Université de Paris-Sud, France; partly by the Danish Natural Sciences Research Council, grant 9700987. 相似文献
9.
Asao Arai 《Integral Equations and Operator Theory》1993,16(1):38-63
LetA andB be anticommuting self-adjoint operators in a Hilbert space . It is proven thatiAB is essentially self-adjoint on a suitable domain and its closureC(A, B) anticommutes withA andB. LetU
s
be the partial isometry associated with the self-adjoint operatorsS, i.e., the partial isometry defined by the polar decompositionS=U
S
|S|. LetP
S
be the orthogonal projection onto (KerS). Then the following are proven: (i) The operatorsU
A
,U
B
,U
C(A,B)
,P
A
,P
B
, andP
A
P
B
multiplied by some constants satisfy a set of commutation relations, which may be regarded as an extension of that satisfied by the standard basis of the Lie algebra
of the special unitary groupSU(2); (ii) There exists a Lie algebra
associated with those operators; (iii) If is separable andA andB are injective, then
gives a completely reducible representation of
with each irreducible component being the spin representation of the Clifford algebra associated with 3; This result can be extended to the case whereA andB are not necessarily injective. Moreover, some properties ofA+B are discussed. The abstract results are applied to Dirac operators. 相似文献
10.
Smaïl Djebali Karima Hammache 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(10):3440-3449
In this work, we present some new versions of fixed point theorems for nonexpansive maps and 1-set contractions defined on closed, convex, not necessarily bounded subsets of Banach spaces. Our proofs rely on a compactness result for an approximate fixed point set. The Kuratowski measure of noncompactness is used throughout. To illustrate the results obtained, some applications to Banach algebras and Hammerstein integral equations are provided. 相似文献
11.
Let (A, –, C) be an abstract dynamical system withA being the generator of aC
0-semigroup on a Hilbert spaceH, C:D(A)Y a linear operator,Y another Hilbert space. In this paper, some sufficient and necessary conditions are obtained for the observation operatorC to be infinite-time admissible. For a control system (A, B, –), due to duality argument, some sufficient and necessary conditions are also given for the control operatorB to be extended admissible. It is wellknown that observation operatorC is admissible if and only if the operator Lyapunov equation associated with the system has a nonnegative solution. In this paper, all nonnegative solutions to this equation are represented parametrically.This project is supported by the NNSF of China, and the Youth Science and Technique Foundation of Shanxi Province. 相似文献
12.
We give a formula for the Lipschitz constant in Thompson's part metric of any order-preserving flow on the interior of a (possibly infinite dimensional) closed convex pointed cone. This shows that in the special case of order-preserving flows, a general characterization of the contraction rate in Thompson's part metric, given by Nussbaum, leads to an explicit formula. As an application, we show that the flow of the generalized Riccati equation arising in stochastic linear quadratic control is a local contraction on the cone of positive definite matrices and characterize its Lipschitz constant by a matrix inequality. We also show that the same flow is no longer a contraction in other invariant Finsler metrics on this cone, including the standard invariant Riemannian metric. This is motivated by a series of contraction properties concerning the standard Riccati equation, established by Bougerol, Liverani, Wojtkowski, Lawson, Lee and Lim: we show that some of these properties do, and that some other do not, carry over to the generalized Riccati equation. 相似文献
13.
Jean Dolbeault Maria J Esteban Michael Loss Luis Vega 《Journal of Functional Analysis》2004,216(1):1-21
We prove some sharp Hardy-type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity. 相似文献
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Igor M. Novitskiî 《Integral Equations and Operator Theory》1999,35(1):93-104
In this paper we describe families of those bounded linear operators that are simultaneously unitarily equivalent to integral operators with smooth Carleman kernels. The singleton case of the main result implies that every integral operator is unitarily equivalent to an integral operator having smooth Carleman kernel. 相似文献
16.
Kristian Bjerklöv David Damanik Russell Johnson 《Annali di Matematica Pura ed Applicata》2008,187(1):1-6
We consider the Lyapunov exponent of those continuous SL $(2,\mathbb{R})We consider the Lyapunov exponent of those continuous SL-valued cocycles over irrational rotations that appear in the study of Schr?dinger operators and prove generic results related
to large coupling asymptotics and uniform convergence. 相似文献
17.
Let H be a finite-dimensional complex Hilbert space. The aim of this paper is to prove that every transformation on the space of all density operators on H which preserves the relative entropy is implemented by either a unitary or an antiunitary operator on H. 相似文献
18.
Anatoliy P. Petravchuk 《Linear algebra and its applications》2010,433(3):574-579
It is well known that each pair of commuting linear operators on a finite dimensional vector space over an algebraically closed field has a common eigenvector. We prove an analogous statement for derivations of k[x] and k[x,y] over any field k of zero characteristic. In particular, if D1 and D2 are commuting derivations of k[x,y] and they are linearly independent over k, then either (i) they have a common polynomial eigenfunction; i.e., a nonconstant polynomial f∈k[x,y] such that D1(f)=λf and D2(f)=μf for some λ,μ∈k[x,y], or (ii) they are Jacobian derivations
19.
Asao Arai 《Integral Equations and Operator Theory》1995,21(2):139-173
LetA andB be two anticommuting self-adjoint operators andV() be a symmetric operator in a Hilbert space, where >0 is a parameter. It is proven that, under some conditions forV(), the resolvents of A+2
B±2|B|+V() converge as . Applications to the nonrelativistic-limit problem of Dirac operators and supersymmetry are discussed.This work is supported by the Grant-In-Aid 0560139 for science research from the Ministry of Education, Japan. 相似文献
20.
Sergey Alexandrovich Buterin 《Results in Mathematics》2007,50(3-4):173-181
The operator of double differentiation perturbed by the composition of a Volterra convolution operator and the differentiation
one on a finite interval with Dirichlet boundary conditions is considered. It is proved that the standard asymptotics is necessary
and sufficient for an arbitrary sequence of complex numbers to be the spectrum of such an operator, which is determined uniquely.
A constructive procedure for solving the inverse problem is given.
Received: March 5, 2007. 相似文献