共查询到20条相似文献,搜索用时 874 毫秒
1.
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
2.
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
3.
Alan McIntosh 《Journal of Functional Analysis》1978,30(2):264-275
It is shown that there is a closed symmetric derivation δ of a C1-algebra with dense domain (δ), an element A = A1 ?(δ), and a C1-function such that (A)?(δ). Some estimates are derived for , where 0 < α < 1. It is shown that there exists a family of one-one self-adjoint operators S(t) in (H) which depends linearly on t, while is not differentiable. It is also shown that there exists (H) which is not C1-self-adjoint even though it satisfies for all t ? 相似文献
4.
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
5.
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
6.
7.
Rahman Younis 《Journal of Functional Analysis》1981,44(3):381-387
The main result of this paper is that if F is a closed subset of the unit circle, then is an M-ideal of . Consequently, if then ? has a closest element in H∞ + LF∞. Furthermore, if is not the dual of any Banach space. 相似文献
8.
Elliptic operators , α a multi-index, with leading term positive and constant coefficient, and with lower order coefficients defined on or a quotient space are considered. It is shown that the Lp-spectrum of A is contained in a “parabolic region” Ω of the complex plane enclosing the positive real axis, uniformly in p. Outside Ω, the kernel of the resolvent of A is shown to be uniformly bounded by an L1 radial convolution kernel. Some consequences are: A can be closed in all Lp (1 ? p ? ∞), and is essentially self-adjoint in L2 if it is symmetric; A generates an analytic semigroup e?tA in the right half plane, strongly Lp and pointwise continuous at t = 0. A priori estimates relating the leading term and remainder are obtained, and summability , with φ analytic, is proved for , with convergence in Lp and on the Lebesgue set of ?. More comprehensive summability results are obtained when A has constant coefficients. 相似文献
9.
Zeev Schuss 《Journal of Mathematical Analysis and Applications》1977,59(2):227-241
Let A and B be uniformly elliptic operators of orders 2m and 2n, respectively, m > n. We consider the Dirichlet problems for the equations (?2(m ? n)A + B + λ2nI)u? = f and (B + λ2nI)u = f in a bounded domain Ω in Rk with a smooth boundary ?Ω. The estimate is derived. This result extends the results of [7, 9, 10, 12, 14, 15, 18]by giving estimates up to the boundary, improving the rate of convergence in ?, using lower norms, and considering operators of higher order with variable coefficients. An application to a parabolic boundary value problem is given. 相似文献
10.
Satendra K Vaish 《Journal of Mathematical Analysis and Applications》1984,101(1):23-29
In this paper we obtain a growth relation for entire functions of qth order with respect to the distribution of its zeros. We also derive certain relations between the qth convergence exponents of two or more entire functions. The most striking result of the paper is: If f(z) has at least one zero, then , where n(r) is the number of zeros of f(z) in and . 相似文献
11.
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
12.
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
13.
Tosio Kato 《Journal of Functional Analysis》1973,12(4):415-417
It is shown that the method of Chernoff developed in the preceding paper can be modified to prove the essential self-adjointness on C0∞(Rm) of all positive powers of the Schrödinger operator T = ? Δ + q if q real and in C∞(Rm) and if . 相似文献
14.
The existence, uniqueness, and construction of unitary n × n matrix valued functions in Wiener-like algebras on the circle with prescribed matrix Fourier coefficients for j ? 0 are studied. In particular, if , then such an ? exists with if and only if ∥Γ0∥ ? 1, where Γv, denotes the infinite block Hankel matrix (γj + k + v), j, k = 0, 1,…, acting in the sequence space ln2. One of the main results is that the nonnegative factorization indices of every such ? are uniquely determined by the given data in terms of the dimensions of the kernels of , whereas the negative factorization indices are arbitrary. It is also shown that there is a unique such ? if and only if the data forces all the factorization indices to be nonnegative and simple conditions for that and a formula for ? in terms of certain Schmidt pairs of Γ0 are given. The results depend upon a fine analysis of the structure of the kernels of and of the one step extension problem of Adamjan, Arov, and Krein (Funct. Anal. Appl.2 (1968), 1–18). Isometric interpolants for the nonsquare case are also considered. 相似文献
15.
Maria Giovanna Garroni Jean Pierre Gossez 《Journal of Mathematical Analysis and Applications》1983,92(1):252-273
This paper is composed of two parts. In the first part closedness and compactness results are given for a sequence of nonlinear elliptic operators of the form , with monotone-type assumptions on the Aα's. These results are then used in the second part to derive existence theorems for a quasi-variational inequality related to some questions from nonlinear heat flow. This quasi-variational inequality involves a second-order operator as above and an implicit obstacle of the Signorini type on the boundary. 相似文献
16.
Derek W Robinson 《Journal of Functional Analysis》1977,24(3):280-290
Let U, V be two strongly continuous one-parameter groups of bounded operators on a Banach space with corresponding infinitesimal generators S, T. We prove the following: ∥Ut, ? Vt ∥ = O(t), t → 0, if and only if U = V; ∥Ut ? Vt∥ = O(tα), t → 0; with 0 ? α ? 1, if and only if , where Ω, P, are bounded operators on such that if and only if has a bounded extension to 1. Further results of this nature are inferred for semigroups, reflexive spaces, Hilbert spaces, and von Neumann algebras. 相似文献
17.
A function f(z) = z ? ∑∞n = 2anzn, an ? 0, analytic and univalent in the unit disk, is said to be in the family , a real and b ? 0, if for all z in the unit disk. A complete characterization is found for when a ? 1. Also, sharp coefficient bounds are determined for certain subclasses of when a < 1; however, examples are given to show that these bounds do not remain valid for the whole family. 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.
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
20.
Abstract connections between integral kernels of positivity preserving semigroups and suitable Lp contractivity properties are established. Then these questions are studied for the semigroups generated by , the Dirichlet Laplacian for an open, connected region Ω. As an application under a suitable hypothesis, Sobolev estimates are proved valid up to ?Ω, of the form , where ?0 is the unique positive L2 eigenfunction of . 相似文献