共查询到20条相似文献,搜索用时 656 毫秒
1.
Lawrence Corwin 《Journal of Functional Analysis》1976,22(1):39-57
Let G be a separable locally compact group with a discrete cocompact subgroup Γ; let N be a normal subgroup of G, and suppose that Γ0 = Γ ∩ N is cocompact in N. Let ? be a finite-dimensional representation of Γ, and let τ = IndΓ → G ?. We investigate the problem of determining the decomposition of τ, given the decomposition of the corresponding representation and certain other facts (essentially those used in the “Mackey machine”). The last section is devoted to a reciprocity theorem for τ. 相似文献
2.
Christopher K.R.T. Jones 《Journal of Differential Equations》1983,49(1):142-169
Two theorems are proved for the spherically symmetric solutions of the “bistable” reaction-diffusion equation , where ? is cubic-like and x ∈ Rn. The first theorem says that, for a suitable class of initial data, there are only two types of asymptotic behavior, u(x, t) tends to an equilibrium solution as t → + ∞ or u(x, t) → 1 uniformly on compact sets. The second theorem says that in the latter case, if the solution is followed out along any ray, it approaches, in shape, the one-dimensional travelling wave. 相似文献
3.
Rachel J Pries 《Comptes Rendus Mathematique》2002,335(5):485-487
Consider a wildly ramified G-Galois cover of curves branched at only one point over an algebraically closed field k of characteristic p. In this note, I prove using formal patching that all sufficiently large conductors occur for such covers φ when the Sylow p-subgroups of G have order p. To cite this article: R.J. Pries, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 485–487. 相似文献
4.
Didier Robert 《Journal of Functional Analysis》1982,45(1):74-94
Let . Under suitable conditions we prove that is a pseudodifferential operator whose symbol has an asymptotic: . More general pseudodifferential operator's classes are also considered. We apply this result to study the semi-classical behaviour of the spectrum of Hv as h → 0. So, we improve recent results obtained by J. Chazarain and by the author in collaboration with B. Helffer. Furthermore we give a precise meaning to the formal development considered in B. Grammaticos and A. Voros' work (Ann. Physics123 (1979), 359–380). 相似文献
5.
Let E be an algebraic (or holomorphic) vectorbundle over the Riemann sphere 1(). Then Grothendieck proved that E splits into a sum of line bundles E = ⊕Li and the isomorphism classes of the Li are (up to order) uniquely determined by E. The Li in turn are classified by an integer (their Chern numbers) so that m-dimensional vectorbundles over 1 are classified by an m-tuple of integers .In this short note we present a completely elementary proof of these facts which, as it turns out, works over any field k. 相似文献
6.
Richard A Alò Charles Cheney Andre de Korvin 《Journal of Mathematical Analysis and Applications》1973,42(1):110-118
In this paper we obtain a Radon-Nikodym theorem for positive linear functionals on a B1-algebra M. Some corollaries analogous to those obtained in the classical case are also obtained here. It is known that if X is a Banach space, then the space of Bochner integrable functions on a probability space Ω with values in X is the completion (in a suitable topology) of the tensor product . Using our theorem, it is possible to extend this result for certain linear mappings from M ? X to X. 相似文献
7.
8.
A continuity theorem for an operator of the form when ? is not a continuous function is proven. 相似文献
9.
Seiya Negami 《Discrete Mathematics》1983,44(2):161-180
A topological generalization of the uniqueness of duals of 3-connected planar graphs will be obtained. A graph G is uniquely embeddable in a surface F if for any two embeddings , , there are an autohomeomorphism h:F → F and an automorphism σ:G → G such that . A graph G is faithfully embedabble in a surface F if there is an embedding such that for any automorphism σ:G → G, there is an autohomeomorphism h:F → F with . Our main theorems state that any 6-connected toroidal graph is uniquelly embeddable in a torus and that any 6-connected toroidal graph with precisely three exceptions is faithfully embeddable in a torus. The proofs are based on a classification of 6-regular torus graphs. 相似文献
10.
Min Ming Tang 《Journal of Mathematical Analysis and Applications》1977,57(2):368-381
In this paper we study the behavior of solutions of some quasilinear parabolic equations of the form as t → ∞. In particular, the solutions of these equations will decay to zero as t → ∞ in the L∞ norm. 相似文献
11.
S.K. Bajpai Joseph Tanne Donald Whittier 《Journal of Mathematical Analysis and Applications》1974,48(3):736-742
Let f(z), an analytic function with radius of convergence R (0 < R < ∞) be represented by the gap series ∑k = 0∞ckzλk. Set and define the growth constants ?, λ, T, t by , and if 0 < ? < ∞, . Then, assuming 0 < t < T < ∞, we obtain a decomposition theorem for f(z). 相似文献
12.
Variational problems for the multiple integral , where and are studied. A new condition on g, called W1,p-quasiconvexity is introduced which generalizes in a natural way the quasiconvexity condition of C. B. Morrey, it being shown in particular to be necessary for sequential weak lower semicontinuity of in and for the existence of minimizers for certain related integrals. Counterexamples are given concerning the weak continuity properties of Jacobians in , p ? n = m. An existence theorem for nonlinear elastostatics is proved under optimal growth hypotheses. 相似文献
13.
Niels Vigand Pedersen 《Journal of Functional Analysis》1981,43(3):368-393
For an arbitrary separable locally compact group G we exhibit a canonical Borel subset of the quasi-dual (with the Mackey Borel structure), such that is a standard Borel space in the induced Borel structure, and such that the canonical measure for the left regular representation λGof G is concentrated on . On the basis of this we discuss the (non-unimodular) “Plancherel theorem.” 相似文献
14.
Consider the renewal equation in the form (1) , where is a probability density on [0, ∞) and limt → ∞g(t) = g0. Asymptotic solutions of (1) are given in the case when f(t) has no expectation, i.e., . These results complement the classical theorem of Feller under the assumption that f(t) possesses finite expectation. 相似文献
15.
W Fernandez de la Vega 《Journal of Combinatorial Theory, Series B》1983,35(3):328-332
For any tournament T on n vertices, let h(T) denote the maximum number of edges in the intersection of T with a transitive tournament on the same vertex set. Sharpening a previous result of Spencer, it is proved that, if Tn denotes the random tournament on n vertices, then, as n → ∞. 相似文献
16.
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
17.
Boguslaw Tomaszewski 《Journal of Functional Analysis》1984,55(1):63-67
It is shown, for n ? m ? 1, that there exist inner maps Φ: Bn → Bm with boundary values such that . where σn and σm are the Haar measures on ?Bn and ?Bm, respectively, and A ? Bn is an arbitrary Borel set. 相似文献
18.
If we change the sign of p ? m columns (or rows) of an m × m positive definite symmetric matrix A, the resultant matrix B has p negative eigenvalues. We give systems of inequalities for the eigenvalues of B and of the matrix obtained from B by deleting one row and column. To obtain these, we first develop characterizations of the eigenvalues of B which are analogous to the minimum-maximum properties of the eigenvalues of a symmetric A, i.e. the Courant-Fischer theorem. These results arose from studying probability distributions on the hyperboloid of revolution . By contrast, the familiar results are associated with the sphere x21 + ? + x2m = 1. 相似文献
19.
J.A.M McHugh 《Journal of Differential Equations》1973,13(2):374-383
Weber's parabolic cylinder equation, , (1) has as solutions the parabolic cylinder functions, , z → + ∞. (7) The expansion (7) is generally not valid for z → ? ∞. This situation leads to the so-called “lateral connection problem” for (1). A novel method of solution of this problem based on the Hadamard factorization theorem applied to the “lateral connection coefficient” is given. Unlike previous methods, explicit contour integrals for Dv(z) are not required. 相似文献
20.
Norbert Herrndorf 《Journal of multivariate analysis》1984,15(1):141-146
In this note a functional central limit theorem for ?-mixing sequences of I. A. Ibragimov (Theory Probab. Appl.20 (1975), 135–141) is generalized to nonstationary sequences (Xn)n ∈ , satisfying some assumptions on the variances and the moment condition for some b > 0, ? > 0. 相似文献