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1.
Wolfgang Ruess 《Journal of Mathematical Analysis and Applications》1981,84(2):400-417
This is a study of compactness in (a) spaces Kb(X, Y) of compact linear operators, (b) injective tensor products , and (c) spaces Lc(X, Y) of continuous linear operators, and its various relationships with equicontinuity and collective compactness. Among the applications is a result on factoring compact sets of compact operators compactly and uniformly through one and the same reflexive Banach space. 相似文献
2.
The main concern of this paper is linear matrix equations with block-companion matrix coefficients. It is shown that general matrix equations AX ? XB = C and X ? AXB = C can be transformed to equations whose coefficients are block companion matrices: and , respectively, where ?L and CM stand for the first and second block-companion matrices of some monic r × r matrix polynomials L(λ) = λsI + Σs?1j=0λjLj and M(λ) = λtI + Σt7minus;1j=0λjMj. The solution of the equat with block companion coefficients is reduced to solving vector equations Sx = ?, where the matrix S is r2l × r2l[l = max(s, t)] and enjoys some symmetry properties. 相似文献
3.
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
4.
Sidney I. Resnick 《Stochastic Processes and their Applications》1973,1(1):67-82
{Xn,n?1} are i.i.d. random variables with continuous d.f. F(x). Xj is a record value of this sequence if Xj>max{X1,…,Xj?1}. Consider the sequence of such record values {XLn,n?1}. Set R(x)=-log(1?F(x)). There exist Bn > 0 such that . in probability (i.p.) iff i.p. iff → ∞ as x→∞ for all k>1. Similar criteria hold for the existence of constants An such that XLn?An → 0 i.p. Limiting record value distributions are of the form N(-log(-logG(x))) where G(·) is an extreme value distribution and N(·) is the standard normal distribution. Domain of attraction criteria for each of the three types of limit laws can be derived by appealing to a duality theorem relating the limiting record value distributions to the extreme value distributions. Repeated use is made of the following lemma: If , then XLn=Y0+…+Yn where the Yj's are i.i.d. and . 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.
David S Jerison 《Journal of Functional Analysis》1981,43(1):97-142
For (x,y,t)∈n × n × , denote and . When α = n ? 2q, a represents the action of the Kohn Laplacian □b on q-forms on the Heisenberg group. For ?n < α < n, we construct a parametrix for the Dirichlet problem in smooth domains D near non-characteristic points of ?D. A point w of ?D is non-characteristic if one of X1,…, Xn, Y1,…, Yn is transverse to ?D at w. This yields sharp local estimates in the Dirichlet problem in the appropriate non-isotropic Lipschitz classes. The main new tool is a “convolution calculus” of pseudo-differential operators that can be applied to the relevant layer potentials, for which the usual asymptotic composition formula is false. Characteristic points are treated in Part II. 相似文献
7.
A compactificaton αX of a completely regular space X is “determined” by a subset F of C1(X) if αX is the smallest compactificaton of X to which each element of F extends, and is “generated” by F if the evaluation map , is an embedding and . Evidently, if F either determines or generates αX, then every elements of F has an extension to αX; whenever F satisfies this latter condition, the set of all such extensions is denoted Fα.A major results of our previous paper is that F determines αX if and only if Fα separates points of αX ? X. A major result of the present paper is that F generates αX if and only if Fα separates points of αX. 相似文献
8.
Young Han Choe 《Journal of Mathematical Analysis and Applications》1985,106(2):293-320
A necessary and sufficient condition that a densely defined linear operator A in a sequentially complete locally convex space X be the infinitesimal generator of a quasi-equicontinuous C0-semigroup on X is that there exist a real number β ? 0 such that, for each λ > β, the resolvent (λI ? A)?1 exists and the family {(λ ? β)k(λI ? A)?k; λ > β, k = 0, 1, 2,…} is equicontinuous. In this case all resolvents (λI ? A)?1, λ > β, of the given operator A and all exponentials exp(tA), t ? 0, of the operator A belong to a Banach algebra which is a subspace of the space L(X) of all continuous linear operators on X, and, for each t ? 0 and for each x?X, one has limk → z (I ? k?1tA)?kx = exp(tA) x. A perturbation theorem for the infinitesimal generator of a quasi-equicontinuous C0-semigroup by an operator which is an element of is obtained. 相似文献
9.
Matania Ben-Artzi 《Journal of Differential Equations》1980,38(1):51-60
Let H = ?Δ + V, where the potential V is spherically symmetric and can be decomposed as a sum of a short-range and a long-range term, V(r) = VS(r) + VL. Let λ = lim supr→∞VL(r) < ∞ (we allow λ = ? ∞) and set λ+ = max(λ, 0). Assume that for some r0, VL(r) ?C2k(r0, ∞) and that there exists δ > 0 such that . Assume further that and that 2kδ > 1. It is shown that: (a) The restriction of H to C∞(Rn) is essentially self-adjoint, (b) The essential spectrum of H contains the closure of (λ, ∞). (c) The part of H over (λ, ∞) is absolutely continuous. 相似文献
10.
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
11.
N.J Kalton 《Journal of Functional Analysis》1981,42(3):299-337
We prove a number of results concerning isomorphisms between spaces of the type Lp(X), where X is a separable p-Banach space and 0 < p < 1. Our results imply that the quotient of Lp([0, 1] × [0, 1]) by the subspace of functions depending only on the first variable is not isomorphic to Lp, answering a question of N. T. Peck. More generally if 0 is a sub-σ-algebra of the Borel sets of [0, 1], then , 0) is isomorphic to Lp if and only if Lp([0, 1], B0) is complemented. We also show that Lp has, up to isomorphism, at most one complemented subspace non-isomorphic to Lp and classify completely those spaces X for which . In particular if then or is finite-dimensional. If X has trivial dual and . 相似文献
12.
Let , let , where g2 and g3 are coefficients of the elliptic curve: Y2 = 4X3 ? g2X ? g3 over a finite field and Δ = g23 ? 27g32 and let . Then the p-adic cohomology theory will be applied to compute explicitly the zeta matrices of the elliptic curves, induced by the pth power map on the free -module . Main results are; Theorem 1.1: X2dY and YdX are basis elements for ; Theorem 1.2: YdX, X2dY, Y?1dX, Y?2dX and XY?2dX are basis elements for , where is a lifting of X, and all the necessary recursive formulas for this explicit computation are given. 相似文献
13.
14.
R.S. Singh 《Journal of multivariate analysis》1976,6(2):338-342
Let Xj = (X1j ,…, Xpj), j = 1,…, n be n independent random vectors. For x = (x1 ,…, xp) in Rp and for α in [0, 1], let Fj(x) = αI(X1j < x1 ,…, Xpj < xp) + (1 ? α) I(X1j ≤ x1 ,…, Xpj ≤ xp), where I(A) is the indicator random variable of the event A. Let Fj(x) = E(Fj(x)) and Dn = supx, α max1 ≤ N ≤ n |Σ0n(Fj(x) ? Fj(x))|. It is shown that P[Dn ≥ L] < 4pL exp{?2(L2n?1 ? 1)} for each positive integer n and for all L2 ≥ n; and, as n → ∞, with probability one. 相似文献
15.
Bent Fuglede 《Journal of Functional Analysis》1974,16(1):101-121
In Rn let Ω denote a Nikodym region (= a connected open set on which every distribution of finite Dirichlet integral is itself in . The existence of n commuting self-adjoint operators such that each Hj is a restriction of (acting in the distribution sense) is shown to be equivalent to the existence of a set Λ ?Rn such that the restrictions to Ω of the functions exp i ∑ λjxj form a total orthogonal family in . If it is required, in addition, that the unitary groups generated by H1,…, Hn act multiplicatively on , then this is shown to correspond to the requirement that Λ can be chosen as a subgroup of the additive group Rn. The measurable sets Ω ?Rn (of finite Lebesgue measure) for which there exists a subgroup Λ ?Rn as stated are precisely those measurable sets which (after a correction by a null set) form a system of representatives for the quotient of Rn by some subgroup Γ (essentially the dual of Λ). 相似文献
16.
Pascal Cherrier 《Journal of Functional Analysis》1983,53(3):231-245
On a compact Kähler manifold of complex dimension m ? 2, let us consider the change of Kähler metric . Let F?C∞(V × R) be a function everywhere > 0 and v a real number ≠ 0. When for all (x, t) ?V × ] ?∞, t0], where C and t0 are constants and , one exhibits a function φ?C∞ (V) such that the determinants of the metrics g and . 相似文献
17.
L.R Bragg 《Journal of Differential Equations》1981,41(3):426-439
Let X be a Banach space, let B be the generator of a continuous group in X, and let A = B2. Assume that D(Ar) is dense in X for r an arbitrarily large positive integer and that a and b are non-negative reals. Solution representations are developed for the abstract differential equation corresponding to initial conditions of the form: (i) u(0+) = φ, u(j)(0+) = 0, j = 1, 2, 3 and (ii) u2(0+) = φ, uj(0+) = 0, j = 0, 1, 3 (with φ∈D(Ar)) for all choices of a and b. 相似文献
18.
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
19.
Hermann König 《Journal of Functional Analysis》1977,24(1):32-51
For an open set Ω ? N, 1 ? p ? ∞ and λ ∈ +, let denote the Sobolev-Slobodetzkij space obtained by completing in the usual Sobolev-Slobodetzkij norm (cf. A. Pietsch, “r-nukleare Sobol. Einbett. Oper., Ellipt. Dgln. II,” Akademie-Verlag, Berlin, 1971, pp. 203–215). Choose a Banach ideal of operators , 1 ? p, q ? ∞ and a quasibounded domain Ω ? N. Theorem 1 of the note gives sufficient conditions on λ such that the Sobolev-imbedding map exists and belongs to the given Banach ideal : Assume the quasibounded domain fulfills condition Ckl for some l > 0 and 1 ? k ? N. Roughly this means that the distance of any to the boundary ?Ω tends to zero as for , and that the boundary consists of sufficiently smooth ?(N ? k)-dimensional manifolds. Take, furthermore, 1 ? p, q ? ∞, p > k. Then, if μ, ν are real positive numbers with λ = μ + v ∈ , μ > λ S(; p,q:N) and v > N/l · λD(;p,q), one has that belongs to the Banach ideal . Here λD(;p,q;N)∈+ and λS(;p,q;N)∈+ are the D-limit order and S-limit order of the ideal , introduced by Pietsch in the above mentioned paper. These limit orders may be computed by estimating the ideal norms of the identity mappings lpn → lqn for n → ∞. Theorem 1 in this way generalizes results of R. A. Adams and C. Clark for the ideals of compact resp. Hilbert-Schmidt operators (p = q = 2) as well as results on imbeddings over bounded domains.Similar results over general unbounded domains are indicated for weighted Sobolev spaces.As an application, in Theorem 2 an estimate is given for the rate of growth of the eigenvalues of formally selfadjoint, uniformly strongly elliptic differential operators with Dirichlet boundary conditions in , where Ω fulfills condition C1l.For an open set Ω in N, let denote the Sobolev-Slobodetzkij space obtained by completing in the usual Sobolev-Slobodetzkij norm, see below. Taking a fixed Banach ideal of operators and 1 ? p, q ? ∞, we consider quasibounded domains Ω in N and give sufficient conditions on λ such that the Sobolev imbedding operator exists and belongs to the Banach ideal. This generalizes results of C. Clark and R. A. Adams for compact, respectively, Hilbert-Schmidt operators (p = q = 2) to general Banach ideals of operators, as well as results on imbeddings over bounded domains. Similar results over general unbounded domains may be proved for weighted Sobolev spaces. As an application, we give an estimate for the rate of growth of the eigenvalues of formally selfadjoint, uniformly strongly elliptic differential operators with Dirichlet boundary conditions in , where Ω is a quasibounded open set in N. 相似文献
20.
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