共查询到20条相似文献,搜索用时 15 毫秒
1.
Mouez Dimassi 《Annales Henri Poincare》2006,7(3):513-525
In the large-coupling constant limit we obtain an asymptotic expansion in powers of
of the derivative of the spectral shift function corresponding to
. Here the potential W(x) is positive and
near infinity for some δ> n and ω0 ∈C∞ (Sn-1).
submitted 18/05/05, accepted 19/10/05 相似文献
2.
3.
The spectral shift function of a Schrödinger operator with a perturbation of definite sign is considered. The asymptotics of the spectral shift function for large coupling constant is studied, and results concerning positive and negative perturbations are compared. A more general case of unperturbed operator given by a function of the Laplacian is discussed. This case explains the dependence of the asymptotics of the spectral shift function on the perturbation potential on the one hand and on the order of the unperturbed operator on the other hand. 相似文献
4.
G. Christoph 《Mathematische Nachrichten》1991,153(1):257-272
Under pseudomoment conditions a non-uniform bound is proved for the remainder in asymptotic expansions with a stable limit law, where the quality of the bound with respect to the number of random variables is as good as that with respect to the argument. Further, a theorem for large deviations in the symmetrical problem is obtained. 相似文献
5.
Let be a domain of
N
. We study the infimum 1(h) of the functional |u|
p
+h
–p
V(x)|u|
p
dx in W
1,p
() for ||u||
LP()= 1 where h > 0 tends to zero and V is a measurable function on . When V is bounded, we describe the behaviour of 1(h), in particular when V is radial and 'slowly' decaying to zero. We also study the limit of 1(h) when h 0 for more general potentials and show a necessary and sufficient condition for 1(h) to be bounded. A link with the tunelling effect is established. We end with a theorem of existence for a first eigenfunction related to 1(h). 相似文献
6.
Lothar Heinrich 《Mathematische Nachrichten》1984,115(1):7-20
We study the order structure induced on a rigged Hilbert space ?? ? χ ? ??′by a self-dual cone in χ. Under the assumption that ?? is a semi-reflexive locally convex vector lattice, and a solid subset of ??′ (we speak then of a rigged Hilbert lattice), we show that ??′ is in fact a nondegenerate partial inner product space. 相似文献
7.
In this paper we use the spectral method to analyse the generalized Kuramoto-Sivashinsky equations. We prove the existence and uniqueness of global smooth solution of the equations. Finally, we obtain the error estimation between spectral approximate solution and exact solution on large time. 相似文献
8.
9.
Brice Camus 《Journal of Fourier Analysis and Applications》2006,12(5):495-515
We establish spectral estimates at a critical energy level for h-pseudo-differential operators. Via a trace formula, we compute
the contribution of isolated (nonextremum) critical points under a condition of "real principal type." The main result holds
for all dimensions, for a singularity of any finite order and can be invariantly expressed in terms of the geometry of the
singularity. When the singularities are not integrable on the energy surface the results are significative since the order
w.r.t. h of the spectral distributions are bigger than in the regular
setting. 相似文献
10.
11.
THE LARGE TIME CONVERGENCE OF SPECTRAL METHOD FOR GENERALIZED KURAMOTO-SIVASHINSKY EQUATION (Ⅱ) 总被引:1,自引:0,他引:1
Xin-ming Xiang 《计算数学(英文版)》1998,16(3):203-212
1.IntroductionInthepaper[1],westudedthegeneralizedKuramotrySivashinskyequationWeProvedtheexistenceanduniquenessofglobalsolutionforperiodicinitialproblemandgavethelargetimeerrorestimationforthesolutionofcontinuousspectralmethod.Theaimofthispaperistostudyfullydiscretespectralmethodandthelongtimebehaviorofthesolutionofthissystem.In61wegiventhelargetimeerrorestimationforfullydiscretesolutionofspectralmethod.In52weprove-theexistenceofapproximateattractorsAN,4anding3weprovetheconvergenceofapproal… 相似文献
12.
《数学季刊》2016,(1):51-59
In this paper, we show the asymptotic limit for the 3D Boussinesq system with zero viscosity limit or zero diffusivity limit. By the classical energy method, we prove that as viscosity(or diffusivity) coefficient goes to zero the solutions of the fully viscous equations converges to those of zero viscosity(or zero diffusivity) equations, which extend the previous results on the asymptotic limit under the conditions of the zero parameter(zero viscosity ν = 0 or zero diffusivity η = 0) in 2D case separately. 相似文献
13.
14.
Sharp asymptotic information is determined for the Gagliardo–Nirenberg embedding constants in high dimension. This analysis is motivated by the earlier observation that the logarithmic Sobolev inequality controls the Nash inequality. Moreover, one sees here that Hardy's inequality can be interpreted as the asymptotic limit of the logarithmic Sobolev inequality. 相似文献
15.
B. Grigelionis 《Acta Appl Math》1999,58(1-3):125-134
A triangular array of independent infinitesimal integer-valued random variables is considered. Asymptotic expansions for the probability distributions of sums of these variables are investigated in the case of the limiting compound Poisson laws. 相似文献
16.
We consider quadratic forms of the type
where Xj are i.i.d. random variables with common distribution F and finite fourth moment,
denotes a symmetric matrix with eigenvalues λ1, ..., λN ordered to be non-increasing in absolute value. We prove explicit bounds in terms of sums of 4th powers of entries of the
matrix A and the size of the eigenvalue λ13 for the approximation of the distribution of Q(F,A) by the distribution of Q (φ, A) where φ is standard Gaussian distribution. In typical cases this error is of optimal order
Supported by the DFG-Forschergruppe FOR 399/1-1 at Bielefeld. Partially supported by INTAS N 03-51-5018.
Partially supported by RFBR and RFBR–DFG, grants NN 02-01-00233, 04-01-04000 相似文献
17.
We consider the Fröhlich model of the polaron, whose path integral formulation leads to the transformed path measure with respect to ℙ that governs the law of the increments of the three-dimensional Brownian motion on a finite interval [−T, T] , and Zα, T is the partition function or the normalizing constant and α > 0 is a constant, or the coupling parameter. The polaron measure reflects a self-attractive interaction. According to a conjecture of Pekar that was proved in [9], exists and has a variational formula. In this article we show that when α > 0 is either sufficiently small or sufficiently large, the limit exists, which is also identified explicitly. As a corollary, we deduce the central limit theorem for under and obtain an expression for the limiting variance. © 2019 the Authors. Communications on Pure and Applied Mathematics is published by the Courant Institute of Mathematical Sciences and Wiley Periodicals, LLC. 相似文献
18.
The bipolaron are two electrons coupled to the elastic deformations of an ionic crystal. We study this system in the Fr?hlich
approximation. If the Coulomb repulsion dominates, the lowest energy states are two well separated polarons. Otherwise the
electrons form a bound pair. We prove the validity of the Pekar–Tomasevich energy functional in the strong coupling limit,
yielding estimates on the coupling parameters for which the binding energy is strictly positive. Under the condition of a
strictly positive binding energy we prove the existence of a ground state at fixed total momentum P, provided P is not too large.
Tadahiro Miyao: This work was supported by Japan Society for the Promotion of Science (JSPS). Permanent address: The graduate
school of natural science and technology, Okayama university, Okayama 700-8530, Japan.
Submitted: December 14, 2006. Accepted: March 20, 2007. 相似文献
19.
20.
递推数列极限的初等求法和收敛渐近性 总被引:1,自引:0,他引:1
借助实例介绍一些非线性递推数列,特别是分式线性递推数列极限的初等求法。就一般分式线性递推数列,明确其收敛渐近性,并通过相关推论展示其应用。 相似文献