共查询到20条相似文献,搜索用时 46 毫秒
1.
Tomas Schonbek 《Journal of Differential Equations》1985,56(2):290-296
New and more elementary proofs are given of two results due to W. Littman: (1) Let . The estimate cannot hold for all u?C0∞(Q), Q a cube in , some constant C. (2) Let n ? 2, p ≠ 2. The estimate cannot hold for all C∞ solutions of the wave equation □u = 0 in ; all t ?; some function C: → . 相似文献
2.
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
3.
It is well known that every weak solution (with boundary values 0) of a semilinear equation is a regular solution if ? fulfils the growth condition . Here 2m is the order of A. In this paper we weaken this condition to . This requires a technique completely different from that which may be applied in case (1). 相似文献
4.
Results on partition of energy and on energy decay are derived for solutions of the Cauchy problem . Here the Aj's are constant, k × k Hermitian matrices, x = (x1,…, xn), t represents time, and u = u(t, x) is a k-vector. It is shown that the energy of Mu approaches a limit , where M is an arbitrary matrix; that there exists a sufficiently large subspace of data ?, which is invariant under the solution group U0(t) and such that depending on ? and that the local energy of nonstatic solutions decays as . More refined results on energy decay are also given and the existence of wave operators is established, considering a perturbed equation at infinity. 相似文献
5.
Teruo Ikebe 《Journal of Functional Analysis》1975,20(2):158-177
A spectral representation for the self-adjoint Schrödinger operator H = ?Δ + V(x), x? R3, is obtained, where V(x) is a long-range potential: , grad , being the Laplace-Beltrami operator on the unit sphere Ω. Namely, we shall construct a unitary operator from PL2(R3) onto being the orthogonal projection onto the absolutely continuous subspace for H, such that for any Borel function α(λ), . 相似文献
6.
According to a result of A. Ghizzetti, for any solution y(t) of the differential equation where , (0 ?i ? n ?1, either y(t) = 0 for t ? 1 or there is an integer r with 0 ? r ? n ? 1 such that exists and ≠0. Related results are obtained for difference and differential inequalities. A special case of the former has interesting applications in the study of orthogonal polynomials. 相似文献
7.
Arthur Lubin 《Journal of Functional Analysis》1974,17(4):388-394
Let m and vt, 0 ? t ? 2π be measures on T = [0, 2π] with m smooth. Consider the direct integral = ⊕L2(vt) dm(t) and the operator on , where e(s, t) = exp ∫st ∫Tdvλ(θ) dm(λ). Let μt be the measure defined by for all continuous ?, and let ?t(z) = exp[?∫ (eiθ + z)(eiθ ? z)?1dμt(gq)]. Call {vt} regular iff for all for 1 a.e. 相似文献
8.
A.M Fink 《Journal of Mathematical Analysis and Applications》1982,90(1):251-258
Presented in this report are two further applications of very elementary formulae of approximate differentiation. The first is a new derivation in a somewhat sharper form of the following theorem of V. M. Olovyani?nikov: LetNn (n ? 2) be the class of functionsg(x) such thatg(x), g′(x),…, g(n)(x) are ? 0, bounded, and nondecreasing on the half-line ?∞ < x ? 0. A special element ofNnis. Ifg(x) ∈ Nnis such that, thenfor
1
. Moreover, if we have equality in (1) for some value of v, then we have there equality for all v, and this happens only if in (?∞, 0].The second application gives sufficient conditions for the differentiability of asymptotic expansions (Theorem 4). 相似文献
9.
V.B Headley 《Journal of Mathematical Analysis and Applications》1985,108(1):283-292
Let D(?) be the Doob's class containing all functions f(z) analytic in the unit disk Δ such that f(0) = 0 and lim on an arc A of ?Δ with length . It is first proved that if f?D(?) then the spherical norm ∥ f ∥ = supz?Δ, where C1 = limn→∞. Next, U represents the Seidel's class containing all non-constant functions f(z) bounded analytic in Δ such that almost everywhere. It is proved that inff?U∥f∥ = 0, and if f has either no singularities or only isolated singularities on ?Δ, then ∥f∥ ? C1. Finally, it is proved that if f is a function normal in Δ, namely, the norm ∥f∥< ∞, then we have the sharp estimate ∥fp∥ ? p∥f∥, for any positive integer p. 相似文献
10.
Christer Borell 《Journal of Mathematical Analysis and Applications》1973,43(2):419-440
Let ψ be convex with respect to ?, B a convex body in Rn and f a positive concave function on B. A well-known result by Berwald states that (1) if ξ is chosen such that .The main purpose in this paper is to characterize those functions f : B → R+ such that (1) holds. 相似文献
11.
Abbas Bahri 《Journal of Functional Analysis》1981,41(3):397-427
We study in this paper problems of the type , Ω bounded ? N, , (I) where is given and where . Our main result is that (I) has an infinite number of solutions for a residual set of ? in . In particular, for many n ∈ there exists an open and dense subset of ? in such that (I) has n distinct solutions for such an ? This result is to be related to the conjecture developed in [1] of the existence of an infinite number of solutions to (I). The proof relies on a general characterization of level sets for a certain class of functionals, when there are no critical value in a large enough interval. In addition to the study of problem (I), we apply this characterization to give another proof (using, e.g., Brouwer's fixed point theorem) for some classical results about even functionals and saddle points. 相似文献
12.
Pascal Cherrier 《Journal of Functional Analysis》1984,57(2):154-206
Nonlinear Neumann problems on riemannian manifolds. Let () be a C∞ compact riemannian manifold of dimension n ? 2 whose boundary B is an (n ? 1)-dimensional submanifold and let be the interior of . Study of Neumann problems of the form: , where, for every are bounded by . Application to the determination of a conformal metric for which the scalar curvature of M and the mean curvature of B take prescribed values. 相似文献
13.
14.
Hartmut Pecher 《Journal of Functional Analysis》1985,63(1):101-122
The scattering operator which belongs to a pair of PDEs consisting of the Klein-Gordon equation and a perturbation of it by a power-like nonlinearity z.hfl;(u) is studied. It is shown that this operator can be defined on a whole neighbourhood of the origin in energy space if , where and the space dimension n ? 2 is arbitrary. 相似文献
15.
Raymond C Roan 《Journal of Functional Analysis》1980,39(1):67-74
Let α ? 0 and let . Then D(α) is a subalgebra of l1. We discuss the weak-1 generators of D(α). We use some of our techniques to prove that if ? is a weak-1 generator of H∞ and ∥ ? ∥∞ ? 1, then the composition operator C? on the Dirichlet space has dense range. 相似文献
16.
Palle E.T. Jorgensen 《Journal of Functional Analysis》1980,39(3):281-307
Let H be a complex Hilbert space, and let Gi, i = 1, 2, be closed and orthogonal subspaces of the product space H × H. The subspace G = G1 ⊕ G2 is called a (graph) perturbation. We give conditions for invariance of regular operators (R.O.) under graph perturbations: When is the perturbation of a R.O. again a R.O.? If N is a Hilbert space we consider R.O. (i.e., densely defined and closed operators T) in H=(N) such that G(T)=G(S)⊕V(M, where G denotes the graph, S is a decomposable operator in H, V a decomposable partial isometry such that the initial space of V(t) is equal to M a.e. t, and finally (M) is the Hardy space of analytic 2 vector functions with values in M ? N × N. Such operators T commute with the bilateral shift U; but, unless M = 0, T does not commute with . Conversely, this is a canonical model for all R.O. with said commutativity properties. Moreover, the model is unique when T is given, and M = G(w) where w is a partial isometry in N. The detailed structure of the model is analyzed in the special case where dim N = dim M = 1. We relate the problem to a condition of Szeg? by showing that T is a is the partial isometry in the special case of dimension one. Szeg?'s conditions enters in a different way in the analysis of the case M = N × N, as well as in the spectral analysis of T. Our results provide an answer to a commutativity problem posed by Fuglede. If T is an arbitrary densely defined operator, and A?B(H) is normal, we prove two theorems stating conditions for the implication . These conditions cannot generally be relaxed. 相似文献
17.
Alexander Litvak Alain Pajor Mark Rudelson Nicole Tomczak-Jaegermann Roman Vershynin 《Comptes Rendus Mathematique》2004,339(1):33-38
Let be the space equipped with a norm 6·6 whose unit ball has a bounded volume ratio with respect to the Euclidean unit ball. Let Γ be any random N×n matrix with N>n, whose entries are independent random variables satisfying some moment assumptions. We show that with high probability Γ is a good isomorphism from the n-dimensional Euclidean space onto its image in : there exist α,β>0 such that for all , . This solves a conjecture of Schechtman on random embeddings of ?2n into ?1N. To cite this article: A. Litvak et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004). 相似文献
18.
Gustavo Perla Menzala 《Journal of Mathematical Analysis and Applications》1983,93(2):385-396
The semilinear wave equation in , is studied where □ denotes the d'Alembertian operator and 1 means spatial convolution. Under mild assumptions on the real-valued function V and 2 ? p ? 3 the well-posedness of the Cauchy problem is proved. Furthermore, some properties of the solutions of the equation are analyzed such as the asymptotic behavior of local energy as in the case of zero mass. Our results extend that of Perla Menzala and Strauss, where case p = 2 was studied. 相似文献
19.
David Gurarie 《Journal of Mathematical Analysis and Applications》1985,108(1):223-229
For elliptic operators on Rn and certain of their singular perturbations relative compactness of B with respect to A is established. This result applies to the study of Lp-spectra of elliptic operators for different p. 相似文献
20.
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