共查询到20条相似文献,搜索用时 31 毫秒
1.
Elliott H Lieb 《Journal of Functional Analysis》1983,51(2):159-165
Let ψ1, …,ψN be orthonormal functions in d and let , or , and let . Lp bounds are proved for p, an example being , with p = d(d ? 2)?1. The unusual feature of these bounds is that the orthogonality of the ψi, yields a factor instead of N, as would be the case without orthogonality. These bounds prove some conjectures of Battle and Federbush (a Phase Cell Cluster Expansion for Euclidean Field Theories, I, 1982, preprint) and of Conlon (Comm. Math. Phys., in press). 相似文献
2.
Hideki Kosaki 《Journal of Functional Analysis》1984,59(1):123-131
Let ?, ψ be elements in the predual of a W1-algebra. For their absolute value parts ¦?¦, ¦ψ¦, the estimate is obtained. 相似文献
3.
Let A denote a decomposable symmetric complex valued n-linear function on Cm. We prove , where · denotes the symmetric product and ? the tensor product. As a consequence we have per , where M is a positive semidefinite Hermitian matrix and per denotes the permanent function. A sufficient condition for equality in the matrix inequality is that M is a nonnegative diagonal matrix. 相似文献
4.
M. Neumann 《Linear algebra and its applications》1976,14(1):41-51
In this paper iterative schemes for approximating a solution to a rectangular but consistent linear system Ax = b are studied. Let A?Cm × nr. The splitting A = M ? N is called subproper if R(A) ? R(M) and . Consider the iteration . We characterize the convergence of this scheme to a solution of the linear system. When A?Rm×nr, monotonicity and the concept of subproper regular splitting are used to determine a necessary and a sufficient condition for the scheme to converge to a solution. 相似文献
5.
I Herbst 《Journal of Functional Analysis》1982,48(2):224-251
Let , with ? a normalized Gaussian. Suppose ≠ 0 and that has no eigenfunctions in L2(3N. If H1ψ = μψ with μ < infσess(H1), then (ψ, e?itHψ) decays exponentially at a rate governed by the positions of the resonances of H. 相似文献
6.
Juan C. Peral 《Journal of Functional Analysis》1980,36(1):114-145
Let u(x, t) be the solution of utt ? Δxu = 0 with initial conditions . Consider the linear operator . (Here g = 0.) We prove for t fixed the following result. Theorem 1: T is bounded in Lp if and only if . Theorem 2: If the coefficients are variables in C and constant outside of some compact set we get: (a) If n = 2k the result holds for . (b) If n = 2k ? 1, the result is valid for . This result are sharp in the sense that for p such that we prove the existence of in such a way that . Several applications are given, one of them is to the study of the Klein-Gordon equation, the other to the completion of the study of the family of multipliers and finally we get that the convolution against the kernel is bounded in H1. 相似文献
7.
This paper considers canonical forms for the similarity action of Gl(n) on : , Those canonical forms are obtained as an application of a more general method to select canonical elements Mc in the orbits of a matrix group G acting on a set of matrices . We define a total order (?) on , different from the lexicographic order l? [0l?x ? x <0, but and consider normalized -elements with a minimal number of parameters: It is shown that the row and column echelon forms, the Jordan canonical form, and “nice” control canonical forms for reachable (A,B)-pairs have a homogeneous interpretation as such (?)-minimal orbit elements. Moreover new canonical forms for the general action (?) are determined via this method. 相似文献
8.
Richard Askey Deborah Tepper Haimo 《Journal of Mathematical Analysis and Applications》1977,59(1):119-129
We study degeneration for ? → + 0 of the two-point boundary value problems , and convergence of the operators T?+ and T?? on 2(?1, 1) connected with them, T?±u := τ?±u for all for all . Here ? is a small positive parameter, λ a complex “spectral” parameter; a, b and c are real ∞-functions, a(x) ? γ > 0 for all x? [?1, 1] and h is a sufficiently smooth complex function. We prove that the limits of the eigenvalues of T?+ and of T?? are the negative and nonpositive integers respectively by comparison of the general case to the special case in which a 1 and b c 0 and in which we can compute the limits exactly. We show that (T?+ ? λ)?1 converges for ? → +0 strongly to (T0+ ? λ)?1 if . In an analogous way, we define the operator T?+, n (n ? in the Sobolev space H0?n(? 1, 1) as a restriction of τ?+ and prove strong convergence of (T+?,n ? λ)?1 for ? → +0 in this space of distributions if . With aid of the maximum principle we infer from this that, if h?1, the solution of τ?+u ? λu = h, u(±1) = A ± B converges for ? → +0 uniformly on [?1, ? ?] ∪ [?, 1] to the solution of xu′ ? λu = h, u(±1) = A ± B for each p > 0 and for each λ ? if ? ?.Finally we prove by duality that the solution of τ??u ? λu = h converges to a definite solution of the reduced equation uniformly on each compact subset of (?1, 0) ∪ (0, 1) if h is sufficiently smooth and if 1 ? ?. 相似文献
9.
Let B be a body in R3 and let S denote the boundary of B. The surface S is described by , where f is an analytic function that is real and positive on (?1, 1) and f(±1) = 0. An algorithm is described for computing the scattered field due to a plane wave incident field, under Leontovich boundary conditions. The Galerkin method of solution used here leads to a block diagonal matrix involving 2M + 1 blocks, each block being of order 2(2N + 1). If, e.g., N = O(M2), the computed scattered field is accurate to within an error bounded by , where C and c are positive constants depending only on f. 相似文献
10.
Keith J. Devlin 《Discrete Mathematics》1975,11(1):9-22
In [5], Erdös and Hajnal formulate the following proposition, which we shall refer to as Φ: If ? is an order-type such that , there is ψ ? ?, |ψ| = ω1, such that . In [2], we showed that if V = L, then ?Φ. We do not know if the assumption V = L can be weakened to CH, or if, in fact, Φ is consistent with CH. However, in this note we show that, relative to a certain large cardinal assumption, Φ is consistent with 2ω = ω2, so that ?Φ is not provable in ZFC alone. Our proof has an interesting model-theoretic consequence, which we mention at the end. 相似文献
11.
Let be a Sturm-Liouville operator acting on functions defined on R. The authors have recently shown how to construct commutative associative algebras of distributions of compact support for which L is a centralizer (in the sense that for distributions f, g of compact support) when q is locally bounded. Here, it is assumed either that q is bounded and is integrable, or that q is of bounded variation. A function ψ is then found such that ψ={μ : μ is a measure on R and | μ |(ψ) < & infin;} becomes a Banach algebra containing the algebra of measures of compact support. The representation theory of ψ is discussed and conditions for its semisimplicity are obtained. 相似文献
12.
Robert S Strichartz 《Journal of Functional Analysis》1982,49(1):91-127
The composition of two Calderón-Zygmund singular integral operators is given explicitly in terms of the kernels of the operators. For φ?L1(Rn) and ε = 0 or 1 and ∝ φ = 0 if ε = 0, let Ker(φ) be the unique function on Rn + 1 homogeneous of degree ?n ? 1 of parity ε that equals φ on the hypersurface x0 = 1. Let Sing(φ, ε) denote the singular integral operator , which exists under suitable growth conditions on ? and φ. Then Sing(φ, ε1) Sing(ψ, ε2)f = ?2π2(∝ φ)(∝ ψ)f + Sing(A, ε1, + ε2)f, where (with notation ). This result is used to show that the mapping ψ → A is a classical pseudo-differential operator of order zero if φ is smooth, with top-order symbol , where θ(ξ) is a cut-off function. These results are generalized to singular integrals with mixed homogeneity. 相似文献
13.
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
14.
Philippe Delanoe 《Journal of Functional Analysis》1982,45(3):403-430
Let (Vn, g) be a C∞ compact Riemannian manifold without boundary. Given the following changes of metric: , where a is a fixed constant, we study the corresponding Monge-Ampère equations (1)±, (2)±. We first solve Eq. (2)?, under some simple assumptions on F?C∞. Then, using an appropriate change of functions that enables us to take advantage of the estimates just carried out for Eq. (2)?, we extend to Eq.(1)? all the results proved in our previous articles [5, 6] for the usual Monge-Ampère equation. Although equation (2)+ is not locally invertible, and does not even admit a solution for all , a similar change of functions leads to partial results about Eq. (1)+, via C2 and C3 estimates for Eq. (2)+. Eventually we give some comments and errata of our previous article (P. Delanoë, J. Funct. Anal.41 (1981), 341–353). 相似文献
15.
Walter Rudin 《Journal of Functional Analysis》1983,50(1):100-126
Let B be the open unit ball of n, n > 1. Let I (for “inner”) be the set of all u ? H °(B) that have a.e. on the boundary S of B. Aleksandrov proved recently that there exist nonconstant u ? I. This paper strengthens his basic theorem and provides further information about I and the algebra Q generated by I. Let XY be the finite linear span of products xy, x ? X, y ? Y, and let be the norm closure, in L∞ = L∞(S), of X. Some results: set I is dense in the unit ball of H∞(B) in the compact-open topology. On is weak1-dense in does not contain . (When .) Every unimodular is a pointwise limit a.e. of products . The zeros of every in the ball algebra (but not of every H∞-function) can be matched by those of some u ? I, as can any finite number of derivatives at 0 if . However, cannot be bounded in B if u ? I is non-constant. 相似文献
16.
David S. Jerison 《Journal of Functional Analysis》1981,43(2):224-257
Let L = ∑j = 1mXj2 be sum of squares of vector fields in n satisfying a Hörmander condition of order 2: span{Xj, [Xi, Xj]} is the full tangent space at each point. A point x??D of a smooth domain D is characteristic if X1,…, Xm are all tangent to ?D at x. We prove sharp estimates in non-isotropic Lipschitz classes for the Dirichlet problem near (generic) isolated characteristic points in two special cases: (a) The Grushin operator in 2. (b) The real part of the Kohn Laplacian on the Heisenberg group in 2n + 1. In contrast to non-characteristic points, C∞ regularity may fail at a characteristic point. The precise order of regularity depends on the shape of ?D at x. 相似文献
17.
Donald L. Iglehart 《Stochastic Processes and their Applications》1973,1(1):11-31
Compound stochastic processes are constructed by taking the superpositive of independent copies of secondary processes, each of which is initiated at an epoch of a renewal process called the primary process. Suppose there are M possible k-dimensional secondary processes {ξv(t):t?0}, v=1,2,…,M. At each epoch of the renewal process {A(t):t?0} we initiate a random number of each of the M types. Let ml:l?1} be a sequence of M-dimensional random vectors whose components specify the number of secondary processes of each type initiated at the various epochs. The compound process we study is , where the ξvlj() are independent copies of ξv,mlv is the vth component of m and {τl:l?1} are the epochs of the renewal process. Our interest in this paper is to obtain functional central limit theorems for {Y(t):t?0} after appropriately scaling the time parameter and state space. A variety of applications are discussed. 相似文献
18.
Harry Dym 《Journal of Functional Analysis》1978,28(1):33-57
Let PT denote the orthogonal projection of L2(R1, dΔ) onto the space of entire functions of exponential type ? T which are square summable on the line with respect to the measure , and let G denote the operator of multiplication by a suitably restricted complex valued function g. It is shown that if is summable, if is locally summable, and if belongs to the span in L∞ of e?iyTH∞:T ? 0, in which h is chosen to be an outer function and h#(γ) agrees with the complex conjugate of h(γ) on the line, then exists and is independent of h for every positive integer n. This extends the range of validity of a formula due to Mark Kac who evaluated this limit in the special case h = 1 using a different formalism. It also extends earlier results of the author which were established under more stringent conditions on h. The conclusions are based in part upon a preliminary study of a more general class of projections. 相似文献
19.
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
20.
Takahiko Nakazi 《Journal of Functional Analysis》1983,53(3):224-230
If φ ∈ L∞, we denote by Tφ the functional defined on the Hardy space H1 by . Let Sφ be the set of functions in H1 which satisfy . It is known that if φ is continuous, then Sφ is weak-1 compact and not empty. For many noncontinuous φ each Sφ is weak-1 compact and not empty. A complete descr ption of Sφ if Sφ is weak-1 compact and not empty is obtained. Sφ is not empty if and only if for some nonzero ? in H1. It is shown that if and , where p is an analytic polynomial and g is a strong outer function, then Sφ is weak-1 compact. As the consequence, if , then Sφ is weak-1 compact. 相似文献