共查询到20条相似文献,搜索用时 31 毫秒
1.
Rhonda J Hughes 《Journal of Functional Analysis》1982,49(3):293-314
Perturbations of and suitable m, by distributions V for which , are shown to correspond to self-adjoint operators Hv, in such a way that Hv depends continuously on V, and agrees with H + V when V is sufficiently regular. These results extend joint work with Irving E. Segal [J. Functional Analysis38 (1980), 71–98], in which perturbations of by distributions V with bounded Fourier transforms in L2(R1) were considered. 相似文献
2.
The initial and boundary value problem for the degenerate parabolic equation vt = Δ(?(v)) + F(v) in the cylinder bounded, for a certain class of point functions ? satisfying ?′(v) ? 0 (e.g., ) is considered. In the case that F(v) sign , the equation has a global time solution. The same is true for α = 1 provided the measure of Ω is sufficiently small. In the case that is nondecreasing a condition is given on the initial state v(x, 0) which implies that the solution must blow up in finite time. The existence of such initial states is discussed. 相似文献
3.
Barry Simon 《Journal of Functional Analysis》1985,63(1):123-136
The two lowest eigenvalues E0(λ), E1(λ) of a symmetric double well tunnelling problem ?Δ + λ2V as λ → ∞ are considered and they are compared to the two lowest eigenvalues is supported away from the well-bottoms of V. We determine the leading exponential splitting of various differences of the four numbers . Related problems are discussed. 相似文献
4.
Yuh-Jia Lee 《Journal of Functional Analysis》1982,47(2):153-164
Let (H, B) be an abstract Wiener pair and pt the Wiener measure with variance t. Let a be the class of exponential type analytic functions defined on the complexification [B] of B. For each pair of nonzero complex numbers α, β and f ? a, we define We show that the inverse α,β?1 exists and there exist two nonzero complex numbers α′,β′ such that . Clearly, the Fourier-Wiener transform, the Fourier-Feynman transform, and the Gauss transform are special cases of α,β. Finally, we apply the transform to investigate the existence of solutions for the differential equations associated with the operator c, where c is a nonzero complex number and c is defined by where Δ is the Laplacian and (·, ·) is the pairing. We show that the solutions can be represented as integrals with respect to the Wiener measure. 相似文献
5.
L.R. Haff 《Journal of multivariate analysis》1977,7(3):374-385
Let Sp×p ~ Wishart (Σ, k), Σ unknown, k > p + 1. Minimax estimators of Σ?1 are given for L1, an Empirical Bayes loss function; and L2, a standard loss function (Ri ≡ E(Li ∣ Σ), i = 1, 2). The estimators are , a, b ≥ 0, r(·) a functional on . Stein, Efron, and Morris studied the special cases and , for certain, a, b. From their work , a = k ? p ? 1, b = p2 + p ? 2; whereas, we prove . The reversal is surprising because a.e. (for a particular L2). Assume (compact) ? , the set of p × p p.s.d. matrices. A “divergence theorem” on functions Fp×p : → implies identities for Ri, i = 1, 2. Then, conditions are given for , i = 1, 2. Most of our results concern estimators with r(S) = t(U)/tr(S), U = p ∣S∣1/p/tr(S). 相似文献
6.
If (,) is a normal j-algebra and b? = {X + ijX;X∈b} then ? is a positive polarization at /tf0 in the sense of Auslander and Kostant. The representation defined as in the orbit theory is shown to be given on a space of holomorphic functions on a Siegel II domain. The Fourier transformation is shown to be an intertwining operator between and for a suitable real polarization . These explicit results are used to deduce the Harish-Chandra conditions defining the holomorphic discrete series of a Semisimple Lie Group. 相似文献
7.
Philip W. Smith 《Journal of Approximation Theory》1974,10(4):337-357
In [3] Golomb describes, for 1 < p < ∞, the Hr,p(R)-extremal extension of a function (i.e., the Hr,p-spline with knots in E) and studies the cone of all such splines. We study the problem of determining when is in Wr,p ≡ Hr,p ∩ Lp. If , then is called a Wr,p-spline, and we denote by the cone of all such splines. If E is quasiuniform, then if and only if . The cone with E quasiuniform is shown to be homeomorphic to lp. Similarly, is homeomorphic to hr,p. Approximation properties of the Wr,p-splines are studied and error bounds in terms of the mesh size are calculated. Restricting ourselves to the case p = 2 and to quasiuniform partitions E, the second integral relation is proved and better error bounds in terms of are derived. 相似文献
8.
David A Senechalle 《Journal of Functional Analysis》1978,27(2):203-214
Let L be a finite-dimensional normed linear space and let M be a compact subset of L lying on one side of a hyperplane through 0. A measure of flatness for M is the number , where the infimum is over all f in which are positive on M. Thus D(M) = 1 if M is flat, but otherwise D(M) > 1. On the other hand, let E(M) be a second measure on M defined as follows: If M is linearly independent, E(M) = 1. If M is linearly dependent, then (1) let Z be a minimal, linearly dependent subset of M; (2) partition Z into mutually exclusive subsets U = {u1, …, up} and V = {v1, …, vq} such that there exist positive coefficients ai and bi for which Σi = 1paiui = Σi = 1qbivi; (3) let ; (4) let E(M) be the supremum of all ratios r which can be formed by steps (1), (2) and (3). The main result of this paper is that these two measures are the same: D(M) = E(M). This result is then used to obtain results concerning the Banach distance-coefficient between an arbitrary finite-dimensional normed linear space and Hilbert space. 相似文献
9.
Alan McIntosh 《Journal of Functional Analysis》1985,61(3):307-327
Consider an elliptic sesquilinear form defined on × by , where is a closed subspace of which contains , Ω is a bounded Lipschitz domain in n, for all ζ?n with ¦ζ¦ = 1. Let L be the operator with largest domain satisfying J[u, v] = (Lu, v) for all υ∈. Then L + λI is a maximal accretive operator in for λ a sufficiently large real number. It is proved that is a bounded operator from to provided mild regularity of the coefficients is assumed. In addition it is shown that if the coefficients depend differentiably on a parameter t in an appropriate sense, then the corresponding square root operators also depend differentiably on t. The latter result is new even when the forms J are hermitian. 相似文献
10.
11.
Barry Simon 《Journal of Functional Analysis》1980,35(2):215-229
We use Brownian motion ideas to study Schrödinger operators . In particular: (a) We prove that limt→∞t?1In ∥ e?tH ∥p,p is p-independent for a very large class of V's where ∥ A ∥p,p = norm of A as an operator from Lpto Lp. (b) For v ? 3 and , we show that sup ∥ e?tH ∥∞,∞ < ∞ if and only if H has no negative eigenvalues or zero energy resonances. (c) We relate the “localization of binding” recently noted by Sigal to Brownian hitting probabilities. 相似文献
12.
William C Troy 《Journal of Differential Equations》1980,36(1):89-98
The boundary value problem where u(? ∞, t′) = v(∞, t′) = 0 andv(? ∞, t′) = u(∞, t′) = 1 for each t′ > 0 has been proposed by Murray as a model for the Belousov-Zhabotinskii chemical reaction. Here u and v are proportional to the concentrations of bromous acid and bromide ion, respectively. We prove that there is a range of values for b and r over which the boundary value problem has traveling wave front solutions. 相似文献
13.
Joel E. Cohen 《Discrete Mathematics》1982,40(1):21-24
Let G be a graph on v labelled vertices with E edges, without loops or multiple edges. Let v → ∞ and let E=E(v) be a function of v such that lim . The limit of the probability that a random graph is a unit interval graph, indifference graph or proper interval graph is exp(?c3). 相似文献
14.
Jean Bourgain 《Comptes Rendus Mathematique》2002,335(6):529-531
We consider quasi-periodic Schrödinger operators H on of the form H=Hλ,x,ω=λv(x+nω)δn,n′+Δ where v is a non-constant real analytic function on the d-torus and Δ denotes the discrete lattice Laplacian on . Denote by Lω(E) the Lyapounov exponent, considered as function of the energy E and the rotation vector . It is shown that for |λ|>λ0(v), there is the uniform minoration for all E and ω. For all λ and ω, Lω(E) is a continuous function of E. Moreover, Lω(E) is jointly continuous in (ω,E), at any point such that k·ω0≠0 for all . To cite this article: J. Bourgain, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 529–531. 相似文献
15.
This paper continues the study of the inverse balayage problem for Markov chains. Let X be a Markov chain with state space , let v be a probability measure on B2 and let M(v) consist of probability measures μ on A whose X-balayage onto B2 is v. The faces of the compact, convex set M(v) are characterized. For fixed μ?M(v) the set M(μ,v) of the measures ? of the form , where S is a randomized stopping time, is analyzed in detail. In particular, its extreme points and edge are explicitly identified. A naturally defined reversed chain X, for which v is an inverse balayage of μ, is introduced and the relation between X and X^ is studied. The question of which admit a natural stopping time of X (not involving an independent randomization) such that , is shown to have rather different answers in discrete and continuous time. Illustrative examples are presented. 相似文献
16.
We investigate the boundary value problem , , u(?∞, t) = v(∞, t) = 0, u(∞, t) = 1, and v(?∞, t) = γ ?t > 0 where r > 0, b > 0, γ > 0 and x?R. This system has been proposed by Murray as a model for the propagation of wave fronts of chemical activity in the Belousov-Zhabotinskii chemical reaction. Here u and v are proportional to the concentrations of bromous acid and bromide ion, respectively. We determine the global stability of the constant solution (u, v) ≡ (1,0). Furthermore we introduce a moving coordinate and for each fixed x?R we investigate the asymptotic behavior of u(x + ct, t) and v(x + ct, t) as t → ∞ for both large and small values of the wave speed c ? 0. 相似文献
17.
R. Srinivasan 《Discrete Mathematics》1979,28(2):213-218
18.
D de Caen 《Journal of Combinatorial Theory, Series B》1983,34(3):340-349
The Turán number T(n, l, k) is the smallest possible number of edges in a k-graph on n vertices such that every l-set of vertices contains an edge. Given a k-graph H = (V(H), E(H)), we let Xs(S) equal the number of edges contained in S, for any s-set S?V(H). Turán's problem is equivalent to estimating the expectation E(Xl), given that min(Xl) ≥ 1. The following lower bound on the variance of Xs is proved: , where m = |E(H)| and . This implies the following: putting t(k, l) = limn→∞T(n, l, k)(kn)?1 then t(k, l) ≥ T(s, l, k)((ks) ? 1)?1, whenever s ≥ l > k ≥ 2. A connection of these results with the existence of certain t-designs is mentioned. 相似文献
19.
Alain A. Lewis 《Mathematical Social Sciences》1985,9(3):197-247
Let 1M be a denumerately comprehensive enlargement of a set-theoretic structure sufficient to model R. If F is an internal 1finite subset of 1N such that , we define a class of 1finite cooperative games having the form , where A(F) is the internal algebra of the internal subsets of F, and is a set-function with , , and . If is the space of S-imputations of a game ΓF(1ν) such that , for some , then we prove that contains two nonempty subsets: and , termed the quasi-kernel and S-bargaining set, respectively. Both and are external solution concepts for games of the form ΓF (1ν) and are defined in terms of predicates that are approximate in infinitesimal terms. Furthermore, if L(Θ) is the Loeb space generated by the 1finitely additive measure space 〈F, A(F), UF〉, and if a game ΓF(1ν) has a nonatomic representation on L(Θ) with respect to S-bounded transformations, then the standard part of any element in is Loeb-measurable and belongs to the quasi-kernel of defined in standard terms. 相似文献
20.
Richard Lavine 《Journal of Functional Analysis》1973,12(1):30-54
Absolute continuity in (0, ∞) for Schrödinger operators ? Δ + V(x), with long range potential V = V1 + V2 such that , ? > 0, as , is shown by proving estimates on resolvents near the real axis. Completeness of the modified wave operators for a superposition of Coulomb potentials also follows. Singular local behavior of V is allowed. 相似文献