共查询到20条相似文献,搜索用时 250 毫秒
1.
O.L. Safronov 《Journal of Mathematical Analysis and Applications》2001,260(2):461
Given two self-adjoint operators A and V = V+ − V− , we study the motion of the eigenvalues of the operator A(t) = A − tV as t increases. Let α > 0 and let λ be a regular point for A. We consider the quantities N+ (V; λ, α), N− (V; λ, α), and N0(V; λ, α) defined as the number of eigenvalues of the operator A(t) that pass point λ from the right to the left, from the left to the right, or change the direction of their motion exactly at point λ, respectively, as t increases from 0 to α > 0. We study asymptotic characteristics of these quantities as α → ∞. In the present paper, the results obtained previously [O. L. Safronov, Comm. Math. Phys.193 (1998), 233–243] are extended and given new applications to differential operators. 相似文献
2.
This paper studies the Multi-Resolution Analyses of multiplicity d (d
*), that is, the families (Vn)n
of closed subspaces in
2(
) such that Vn Vn + 1, Vn + 1 = DVn, where Dƒ(x) = ƒ(2x), and such that there exists a Riesz basis for V0 of the form {φi(· − k), i = 1, . . . , d,k
}, with φ1, . . . , φd V0. Using the Fourier transform, we prove that
(λ) = t[
1(λ), . . . ,
d(λ)] = H(λ/2)
(λ/2), where H is in the set
d of continuous 1-periodic functions taking values in
(d,
). If d = 1, the definition corresponds to the standard Multi-Resolution Analyses, and one can characterize the regular 1-periodic complex-valued functions H (called, then, scaling filters) which yield a Multi-Resolution Analysis. In this paper, we generalize this study to d ≥ 2 by giving conditions on H
d so that there exists
= t[
1, . . . ,
d] in
2(
,
d) solution of
(λ) = H(λ/2)
(λ/2), and so that the integer translates of φ1, . . . , φd form a Riesz family. Then, the latter span the space V0 of a Multi-Resolution Analysis of multiplicity d. We show that the conditions on H focus on the zeros of det H(·) and on simple spectral hypotheses for the operator PH defined on
d by PHF(λ) = H(λ/2)F(λ/2)H(λ/2)* + H(λ/2 + 1/2)F(λ/2 + 1/2)H(λ/2 + 1/2)*. Finally, we explore connections with the order r dyadic interpolation schemes, where r
*. 相似文献
3.
We study the Hamiltonian system (HS)
where H ε C2 (
2N,
) satisfies H (0) = 0, H′ (0) = 0 and the quadratic form
) is non-degenerate. We fix τ0 > 0 and assume that
2N E F decomposes into linear subspaces E and F which are invariant under the flow associated to the linearized system (LHS)
= JH″ (0) x and such that each solution of (LHS) in E is τ0-periodic whereas no solution of (LHS) in F − 0 is τ0-periodic. We write σ(τ0) = σQ(τ0) for the signature of the quadratic form Q restricted to E. If σ(τ0) ≠ 0 then there exist periodic solutions of (HS) arbitrarily close to 0. More precisely we show, either there exists a sequence xk → 0 of τk-periodic orbits on the energy level H−1 (0) with τk → τ0; or for each λ close to 0 with λσ(τ0) > 0 the energy level H−1 (λ) contains at least
distinct periodic orbits of (HS) near 0 with periods near τ0. This generalizes a result of Weinstein and Moser who assumed QE to be positive definite. 相似文献
4.
In a sequence ofn independent random variables the pdf changes fromf(x, 0) tof(x, 0 + δvn−1) after the firstnλ variables. The problem is to estimateλ (0, 1 ), where 0 and δ are unknownd-dim parameters andvn → ∞ slower thann1/2. Letn denote the maximum likelihood estimator (mle) ofλ. Analyzing the local behavior of the likelihood function near the true parameter values it is shown under regularity conditions that ifnn2(− λ) is bounded in probability asn → ∞, then it converges in law to the timeT(δjδ)1/2 at which a two-sided Brownian motion (B.M.) with drift1/2(δ′Jδ)1/2ton(−∞, ∞) attains its a.s. unique minimum, whereJ denotes the Fisher-information matrix. This generalizes the result for small change in mean of univariate normal random variables obtained by Bhattacharya and Brockwell (1976,Z. Warsch. Verw. Gebiete37, 51–75) who also derived the distribution ofTμ forμ > 0. For the general case an alternative estimator is constructed by a three-step procedure which is shown to have the above asymptotic distribution. In the important case of multiparameter exponential families, the construction of this estimator is considerably simplified. 相似文献
5.
L∞ estimates are derived for the oscillatory integral ∫+0∞e−i(xλ + (1/m) tλm)a(λ) dλ, where 2 ≤ m
and (x, t)
×
+. The amplitude a(λ) can be oscillatory, e.g., a(λ) = eit
(λ) with
(λ) a polynomial of degree ≤ m − 1, or it can be of polynomial type, e.g., a(λ) = (1 + λ)k with 0 ≤ k ≤
(m − 2). The estimates are applied to the study of solutions of certain linear pseudodifferential equations, of the generalized Schrödinger or Airy type, and of associated semilinear equations. 相似文献
6.
Let X1,…, Xn be i.i.d. random variables symmetric about zero. Let Ri(t) be the rank of |Xi − tn−1/2| among |X1 − tn−1/2|,…, |Xn − tn−1/2| and Tn(t) = Σi = 1nφ((n + 1)−1Ri(t))sign(Xi − tn−1/2). We show that there exists a sequence of random variables Vn such that sup0 ≤ t ≤ 1 |Tn(t) − Tn(0) − tVn| → 0 in probability, as n → ∞. Vn is asymptotically normal. 相似文献
7.
We consider the Tikhonov regularizer fλ of a smooth function f ε H2m[0, 1], defined as the solution (see [1]) to We prove that if f(j)(0) = f(j)(1) = 0, J = m, …, k < 2m − 1, then ¦f − fλ¦j2 Rλ(2k − 2j + 3)/2m, J = 0, …, m. A detailed analysis is given of the effect of the boundary on convergence rates. 相似文献
8.
Let {vij; i, J = 1, 2, …} be a family of i.i.d. random variables with E(v114) = ∞. For positive integers p, n with p = p(n) and p/n → y > 0 as n → ∞, let Mn = (1/n) Vn VnT , where Vn = (vij)1 ≤ i ≤ p, 1 ≤ j ≤ n, and let λmax(n) denote the largest eigenvalue of Mn. It is shown that
a.s. This result verifies the boundedness of E(v114) to be the weakest condition known to assure the almost sure convergence of λmax(n) for a class of sample covariance matrices. 相似文献
9.
F. Mricz 《Journal of multivariate analysis》1989,30(2)
This is a systematic and unified treatment of a variety of seemingly different strong limit problems. The main emphasis is laid on the study of the a.s. behavior of the rectangular means ζmn = 1/(λ1(m) λ2(n)) Σi=1m Σk=1n Xik as either max{m, n} → ∞ or min{m, n} → ∞. Here {Xik: i, k ≥ 1} is an orthogonal or merely quasi-orthogonal random field, whereas {λ1(m): m ≥ 1} and {λ2(n): n ≥ 1} are nondecreasing sequences of positive numbers subject to certain growth conditions. The method applied provides the rate of convergence, as well. The sufficient conditions obtained are shown to be the best possible in general. Results on double subsequences and 1-parameter limit theorems are also included. 相似文献
10.
We study the asymptotic behavior of the ground-state wave function of multiparticle quantum systems without statistics in that region of configuration space where the particles break up into two well-defined clusters very far apart. One example of our results is the following: consider a system of N particles moving in three dimensions with rotationally invariant two-body potentials which are bounded and have compact support. Let D = C1,C2 be a partition into two clusters so that H(C1) and H(C2) have discrete ground states η1 and η2 of energy ε1 and ε2. Suppose that Σ = ε1 + ε2 = inf σess(H) and that H has a discrete ground state of energy E. Let ζ1and ζ2 denote internal coordinates for the clusters C1 and c2 and let R be the difference of the centers of mass of the clusters. Let μ = M1M2/M1 + M2with Mi the mass of clusters Ci and define k by k2/2m = Σ-E. Then as R → a8 with ¦ζi¦ bounded, we prove that (ζ1,ζ2, R) = cη(ζ1)η(ζ2)e−kRR−1(1+O(e−γR)) for some γ, c > 0. We prove weaker conclusions under weaker hypotheses, including results in the atomic case. 相似文献
11.
B. Feigin M. Jimbo M. Kashiwara T. Miwa E. Mukhin Y. Takeyama 《European Journal of Combinatorics》2004,25(8):1197
Let V(Λi) (resp., V(−Λj)) be a fundamental integrable highest (resp., lowest) weight module of
. The tensor product V(Λi)V(−Λj) is filtered by submodules
, n≥0, n≡i−j mod 2, where viV(Λi) is the highest vector and
is an extremal vector. We show that Fn/Fn+2 is isomorphic to the level 0 extremal weight module V(n(Λ1−Λ0)). Using this we give a functional realization of the completion of V(Λi)V(−Λj) by the filtration (Fn)n≥0. The subspace of V(Λi)V(−Λj) of
-weight m is mapped to a certain space of sequences (Pn,l)n≥0,n≡i−jmod2,n−2l=m, whose members Pn,l=Pn,l(X1,…,Xlz1,…,zn) are symmetric polynomials in Xa and symmetric Laurent polynomials in zk, with additional constraints. When the parameter q is specialized to
, this construction settles a conjecture which arose in the study of form factors in integrable field theory. 相似文献
12.
B. Ricceri 《Mathematical and Computer Modelling》2000,32(11-13)
In this paper, we consider a problem of the type −Δu = λ(f(u) + μg(u)) in Ω, u¦∂Ω = 0, where Ω Rn is an open-bounded set, f, g are continuous real functions on R, and λ, μ ε R. As an application of a new approach to nonlinear eigenvalues problems, we prove that, under suitable hypotheses, if ¦μ¦ is small enough, then there is some λ > 0 such that the above problem has at least three distinct weak solutions in W01,2(Ω). 相似文献
13.
Athanassios G. Kartsatos Richard D. Mabry 《Journal of Mathematical Analysis and Applications》1986,120(2)
The equation (*) Au − λTu + μCu = f is studied in a real separable Hilbert space H. Here, λ, μ > 0 are fixed constants and f ε H is fixed. The operators A: D H → H, C: D H → H are monotone and compact, respectively, where D denotes a closed ball in H. The operator T: H → H is linear, compact, self-adjoint and positive-definite. Degree-theoretic arguments are used for the existence of solutions of (*) and extensions of recent results of Kesavan are established. For example, it is shown, under additional assumptions, that there exists a constant μ0 > 0 such that (*) is solvable for all μ μ0 and all λ ε R. 相似文献
14.
The authors consider the semilinear SchrSdinger equation
-△Au+Vλ(x)u= Q(x)|u|γ-2u in R^N,
where 1 〈 γ 〈 2* and γ≠ 2, Vλ= V^+ -λV^-. Exploiting the relation between the Nehari manifold and fibrering maps, the existence of nontrivial solutions for the problem is discussed. 相似文献
-△Au+Vλ(x)u= Q(x)|u|γ-2u in R^N,
where 1 〈 γ 〈 2* and γ≠ 2, Vλ= V^+ -λV^-. Exploiting the relation between the Nehari manifold and fibrering maps, the existence of nontrivial solutions for the problem is discussed. 相似文献
15.
M. Deza 《Journal of Combinatorial Theory, Series A》1976,20(3):306-318
Le nombre maximal de lignes de matrices seront désignées par:
- 1. (a) R(k, λ) si chaque ligne est une permutation de nombres 1, 2,…, k et si chaque deux lignes différentes coïncide selon λ positions;
- 2. (b) S0(k, λ) si le nombre de colonnes est k et si chaque deux lignes différentes coïncide selon λ positions et si, en plus, il existe une colonne avec les éléments y1, y2, y3, ou y1 = y2 ≠ y3;
- 3. (c) T0(k, λ) si c'est une (0, 1)-matrice et si chaque ligne contient k unités et si chaque deux lignes différentes contient les unités selon λ positions et si, en plus, il existe une colonne avec les éléments 1, 1, 0.
16.
Donglong Li Zhengde Dai Xuhong Liu 《Journal of Mathematical Analysis and Applications》2007,330(2):934-948
In this paper, the two-dimensional generalized complex Ginzburg–Landau equation (CGL)
ut=ρu−Δφ(u)−(1+iγ)Δu−νΔ2u−(1+iμ)|u|2σu+αλ1(|u|2u)+β(λ2)|u|2