共查询到20条相似文献,搜索用时 15 毫秒
1.
Ronald J Stern 《Journal of Mathematical Analysis and Applications》1982,86(1):20-29
Given a set X ? Rn and a subspace B ? Rn, we say that X is -decomposable if there exists a direct sum complement of such that {X ∩ M ≠ ?} and X ? {X ∩ M} + B. A structural characterization of -decomposability is obtained for compact convex X, which yields a procedure for verification of the property in case X is also polyhedral. Our application of -decomposability is in control theory. It is proven that if a compact convex polyhedral set X is {Range(B)}-decomposable, then the system capability of weak invariance (holdability) of X under the linear autonomous control system x = Ax + Bu (without control restraints) is equivalent to the existence of a constant linear feedback law u = Fx under which X is holdable. 相似文献
2.
Let be a strongly equicontinuous Boolean algebra of projections on the quasi-complete locally convex space X and assume that the space L(X) of continuous linear operators on X is sequentially complete for the strong operator topology. Methods of integration with respect to spectral measures are used to show that the closed algebra generated by in L(X) consists precisely of those continuous linear operators on X which leave invariant each closed -invariant subspace of X. 相似文献
3.
Jesper Michael Møller 《Topology and its Applications》1983,16(3):279-286
Let π: E→X be a principal n-bundle and p:V→X an m-dimensional complex vector bundle over, say, a connected CW-complex X. An equivariant embedding of π into p is an embedding h:E → V commuting with projections such that h(e · z)=zh(e) for all eεE and . We compute the primary obstruction to embedding π equivariantly into p. If dim X?2m, then c=0 if and only if π admits an equivariant embedding into p. If dim X>2m and π embeds equivariantly into p, then c=0. Other embedding criteria exist in case p is the trivial m-plane bundle εm. We use these criteria for a discussion of the classification of the equivalence classes of principal -bundles that admit equivariant embeddings into εm. Finally, we offer an example of a principal -bundle that admit an ordinary but not an equivariant embedding into ε1. 相似文献
4.
Harry E Hürzeler 《Journal of multivariate analysis》1984,14(1):34-73
The concept of a quasimartingale, and therefore also of a function of bounded variation, is extended to processes with a regular partially ordered index set V and with values in a Banach space. We show that quasimartingales can be described by their associated measures, defined on an inverse limit space containing , furnished with the σ-algebra of the predictable sets. With the help of this measure, a Rao-Krickeberg and a Riesz decomposition is obtained, as well as a convergence theorem for quasimartingales. For a regular quasimartingale X it is proven that the spaces (, ) and the measures associated with X are unique up to isomorphisms. In the case V = +n we prove a duality between classical (right-) quasimartingales and left-quasimartingales. 相似文献
5.
《Topology and its Applications》2004,135(1-3):231-247
A topological system (X,f) is -transitive if for each pair of opene subsets U and V of X, , where is a collection of subsets of which is hereditary upward. (X,f) is -mixing if (X×X,f×f) is -transitive. In this paper -mixing systems are characterized in terms of the chaoticity of the systems. Moreover, weak disjointness is studied via family. We will give conditions such that a dual theorem of the Weiss–Akin–Glasner theorem holds. Examples with this dual theorem fails for some “good” families are obtained. 相似文献
6.
We consider an extremal problem for directed graphs which is closely related to Turán's theorem giving the maximum number of edges in a graph on n vertices which does not contain a complete subgraph on m vertices. For an integer n?2, let Tn denote the transitive tournament with vertex set Xn={1,2,3,…,n} and edge set {(i,j):1?i<j?n}. A subgraph H of Tn is said to be m-locally unipathic when the restriction of H to each m element subset of Xn consisting of m consecutive integers is unipathic. We show that the maximum number of edges in a m-locally unipathic subgraph of Tn is ( where n= q(m?1+r and . As is the case with Turán's theorem, the extremal graphs for our problem are complete multipartite graphs. Unlike Turán's theorem, the part sizes will not be uniform. The proof of our principal theorem rests on a combinatorial theory originally developed to investigate the rank of partially ordered sets. 相似文献
7.
John Phillips 《Journal of Functional Analysis》1973,13(4):390-409
Let be an achieved left Hilbert algebra. Let be an element such that π′(η) is a positive operator. Then, following M. A. Rieffel, η is called integrable if sup{(η|e)e∈U and ee?e2} < + ∞. It is shown that η is integrable if and only if there is an element ζ∈Dflat; such π′(ζ) is positive and ζ is a square root of η in an appropriate sense. This is shown to be a generalization of Godement's well known theorem on the existence of a convolution square root for a continuous square-integrable positive-definite function on a locally compact group. An “integral” and an “L1-norm” are then defined on the linear span of the positive integrable elements and the completion of this space, denoted by L1(), is shown to be the predual of (). “Godement's theorem” is then used to investigate square-integrable representations of . 相似文献
8.
Michel Las Vergnas 《Discrete Mathematics》1978,23(3):241-255
We prove the following theorem: Let G be a graph with vertex-set V and ?, g be two integer-valued functions defined on V such that for all x ∈ V. Then G contains a factor F such that for all x ∈ V if and only if for every subset X of V, is at least equal to the number of connected components C of G[V ? X] such that either C = {x} and g(x) = 1, or |C| is odd ?3 and for all x ∈ C. Applications are given to certain combinatorial geometries associated with factors of graphs. 相似文献
9.
Mau-Hsiang Shih Kok-Keong Tan 《Journal of Mathematical Analysis and Applications》1985,108(2):333-343
Let E be a Hausdorff topological vector space and X ? E an arbitrary nonempty set. Denote by E′ the dual space of E and the pairing between E′ and E by 〈w, x〉 for w?E′ and x?E. Given a point-to-set map S: X → 2X and a point-to-set map T: X → 2E′, the generalized quasi-variational inequality problem (GQVI) is to find a point and a point such that for all . By using the Ky Fan minimax principle or its generalized version as a tool, some general theorems on solutions of the GQVI in locally convex Hausdorff topological vector spaces are obtained which include a fixed point theorem due to Ky Fan and I. L. Glicksberg, and two different multivalued versions of the Hartman-Stampacchia variational inequality. 相似文献
10.
Ivan Singer 《Journal of Mathematical Analysis and Applications》1980,76(2):339-368
We show that, if (F →uX) is a linear system, a convex target set and a convex functional, then, under suitable assumptions, the computation of inf ) can be reduced to the computation of the infimum of h on certain strips or hyperplanes in F, determined by elements of , or of the infima on F of Lagrangians, involving elements of . Also, we prove similar results for a convex system (F →uX) and the convex cone Ω of all non-positive elements in X. 相似文献
11.
Let X be a complex Banach space and a domain in the complex plane. Let f: → X be an analytic function such that ∥f(ζ)∥ is constant as ζ ? . If X is the complex plane, then by the classical maximum modulus theorem f;(ζ) itself is constant on . This is not the case in general. In the paper we study the norm-constant analytic functions whose values are bounded linear operators over an uniformly convex complex Banach space or, in particular, over a complex Hilbert space. 相似文献
12.
Maurice J Dupré 《Journal of Functional Analysis》1976,22(3):295-322
A Hilbert bundle (p, B, X) is a type of fibre space p: B → X such that each fibre p?1(x) is a Hilbert space. However, p?1(x) may vary in dimension as x varies in X, even when X is connected. We give two “homotopy” type classification theorems for Hilbert bundles having primarily finite dimensional fibres. An (m, n)-bundle over the pair (X, A) is a Hilbert bundle over (p, B, X) such that the dimension of p?1(x) is m for x in A and n otherwise. As a special case, we show that if X is a compact metric space, C+X the upper cone of the suspension SX, then the isomorphism classes of (m, n)-bundles over (SX, C+X) are in one-to-one correspondence with the members of [X, Vm(n)] where Vm(n) is the Stiefel manifold. The results are all applicable to the classification of separable, continuous trace C1-algebras, with specific results given to illustrate. 相似文献
13.
Let Mm,n(F) denote the space of all mXn matrices over the algebraically closed field F. A subspace of Mm,n(F), all of whose nonzero elements have rank k, is said to be essentially decomposable if there exist nonsingular mXn matrices U and V respectively such that for any element A, UAV has the form where A1 is iX(k–i) for some i?k. Theorem: If is a space of rank k matrices, then either is essentially decomposable or dim ?k+1. An example shows that the above bound on non-essentially-decomposable spaces of rank k matrices is sharp whenever n?2k–1. 相似文献
14.
Mo Tak Kiang 《Journal of Mathematical Analysis and Applications》1976,56(3):567-569
Let K be a subset of a Banach space X. A semigroup = {?α ∥ α ∞ A} of Lipschitz mappings of K into itself is called eventually nonexpansive if the family of corresponding Lipschitz constants satisfies the following condition: for every ? > 0, there is a γ?A such that kβ < 1 + ? whenever ?β ? ?γ = {?gg?α ¦ ?α ? }. It is shown that if K is a nonempty, closed, convex, and bounded subset of a uniformly convex Banach space, and if :K → K is an eventually nonexpansive, commutative, linearly ordered semigroup of mappings, then has a common fixed point. This result generalizes a fixed point theorem by Goebel and Kirk. 相似文献
15.
J.R. Tort 《Discrete Mathematics》1983,44(2):181-185
Let X be a set of n elements. Let 3(X) be the set of all triples of X. We define a clique as a set of triples which intersect pairwise in two elements. In this paper we prove that if n?6, the minimum cardinality of a partition of 3(X) into cliques is . 相似文献
16.
17.
For a class of subsets of a set X, let V() be the smallest n such that no n-element set F?X has all its subsets of the form A ∩ F, A ∈ . The condition V() <+∞ has probabilistic implications. If any two-element subset A of X satisfies both A ∩ C = Ø and A ? D for some C, D∈, then if and only if is linearly ordered by inclusion. If is of the form , i=1,2,…,n}, where each is linearly ordered by inclusion, then . If H is an (n-1)-dimensional affine hyperplane in an n-dimensional vector space of real functions on X, and is the collection of all sets {x: f(x)>0} for f in H, then . 相似文献
18.
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
19.
H.H. Hung 《Topology and its Applications》1982,14(2):163-165
We propose a generalization of Heath's theorem that semi-metric spaces with point-countable bases are developable: A semi-metrizable space X is developabale if (and only if) there is on it a σ-discrete family of closed sets, interior-preserving over each member C of which is a countable family {n(C): n ∈ N} of collections of open sets such that if U is a neighbourhood of ξ∈X, then there are such a Γ∈ and such a v∈ N that ξ ? Γ and ξ∈ int ∩ (D: ξ: D∈v(Γ))?U. 相似文献
20.
Simeon M. Berman 《Journal of multivariate analysis》1978,8(1):30-44
Let R(s, t) be a continuous, nonnegative, real valued function on a ≤ s ≤ t ≤ b. Suppose , , and in the interior of the domain. Then the extension of R to a symmetric function on [a, b] × [a, b] is a covariance function. Such a covariance is called biconvex. Let X(t) be a Gaussian process with mean 0 and biconvex covariance. X has a representation as a sum of simple moving averages of white noises on the line and plane. The germ field of X at every point t is generated by X(t) alone. X is locally nondeterministic. Under an additional assumption involving the partial derivatives of R near the diagonal, the local time of the sample function exists and is jointly continuous almost surely, so that the sample function is nowhere differentiable. 相似文献