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1.
For a separable Hilbert space E whose dimension is 2 and for an open subset of E, not empty and different from E, let be the set of all points of which have at least two projections on the close set E\, and let be the set of all the centres of the open balls contained in and which are maximal for inclusion. We show that the Hausdorff dimension dimH( ) of may be any real value s such that 0sdim E; we also show that can be chosen so that is everywhere dense in and so that we have dimH( )=1.Associons à un ouvert d'un espace de Hilbert séparable E de dimension 2, non vide et distinct de E, l'ensemble des points de admettant plusieurs projections sur le fermé E\, et l'ensemble des centres des boules ouvertes inclues dans et maximales pour l'inclusion. Nous montrons d'une part que la dimension de Hausdorff dimH( ) de peut prendre toute valeur réelle s telle que 0sdim E, et d'autre part qu'on peut choisir de sorte que soit dense dans et qu'on ait dimH( )=1.  相似文献   

2.
Let be a real Banach space and let E be an ideal of L 0 over a -finite measure space (, , ). Let (X) be the space of all strongly -measurable functions f: X such that the scalar function , defined by , belongs to E. The paper deals with strong topologies on E(X). In particular, the strong topology the order continuous dual of E(X)) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies.  相似文献   

3.
We consider the boundary value problem in a bounded, smooth domain in with homogeneous Dirichlet boundary conditions. Here 0,k(x) $$ " align="middle" border="0"> is a non-negative, not identically zero function. We find conditions under which there exists a solution which blows up at exactly m points as and satisfies . In particular, we find that if , 0 $" align="middle" border="0"> and is not simply connected then such a solution exists for any given Received: 11 February 2004, Accepted: 17 August 2004, Published online: 22 December 2004  相似文献   

4.
5.
We obtain necessary and sufficient conditions for the solvability of the augmentation and modification problems of order for Hermitian matrices. The augmentation problem consists in the construction of a Hermitian -matrix with a given -block in block -representation and with the prescribed eigenvalues. The modification problem consists in the construction of a Hermitian -matrix of rank not greater than so that the obtained matrix, being added to a given Hermitian -matrix , will have the required spectrum. We give an estimate for the minimal number of different eigenvalues of the solutions to these problems.  相似文献   

6.
For 2-periodic functions and arbitrary q [1, ] and p (0, ], we obtain the new exact Kolmogorov-type inequality which takes into account the number of changes in the sign of the derivatives (x (k)) over the period. Here, = (rk + 1/q)/(r + 1/p), r is the Euler perfect spline of degree r, and . The inequality indicated turns into the equality for functions of the form x(t) = a r (nt + b), a, b R, n N. We also obtain an analog of this inequality in the case where k = 0 and q = and prove new exact Bernstein-type inequalities for trigonometric polynomials and splines.  相似文献   

7.
Let (, ) be a measurable space and C a nonempty bounded closed convex separable subset of p-uniformly convex Banach space E for some p > 1. We prove random fixed point theorems for a class of mappings T: × C C satisfying: for each x, y C, and integer n 1,
where a, b, c: [0, ) are functions satisfying certain conditions and T n(, x) is the value at x of the n-th iterate of the mapping T(, ·). Further we establish for these mappings some random fixed point theorems in a Hilbert space, in L p spaces, in Hardy spaces H p and in Sobolev spaces H k,p for 1 < p < and k 0. As a consequence of our main result, we also extend the results of Xu [43] and randomize the corresponding deterministic ones of Casini and Maluta [5], Goebel and Kirk [13], Tan and Xu [37], and Xu [39, 41].  相似文献   

8.
Let G be a noncompact locally compact group. We show that a necessary and sufficient condition in order that G support an adapted probability measure whose concentration functions fail converge to zero is that G be the semidirect product , where is an automorphism of N contractive modulo a compact subgroup. Any adapted a probability measure whose concentration functions fail to converge to zero has the form =v×1 where v is a probability measure on N. If G is unimodular then the concentration functions of an adapted probability measure fail to converge to zero if and only if is supported on a coset of a compact normal subgroup.  相似文献   

9.
10.
In this paper, oscillation and asymptotic behaviour of solutions of have been studied under suitable assumptions on the coefficient functions such that a(t 0, b(t) 0 and c(t) < 0.  相似文献   

11.
Classical theorems on differential inequalities [1, 2, 3] are generalized for initial value problems of the kind and where is a singular Volterra operator, is continuous and positive on ]a, b], is a norm in R n, and [u]+ and [u] are respectively the positive and the negative part of the vector u R n.  相似文献   

12.
Gábor Czédli 《Order》1994,11(4):391-395
The quasiorders of a setA form a lattice Quord(A) with an involution –1={x, y: y, x}. Some results in [1] and Chajda and Pinus [2] lead to the problem whether every lattice with involution can be embedded in Quord(A) for some setA. Using the author's approach to the word problem of lattices (cf. [3]), which also applies for involution lattices, it is shown that the answer is negative.Research supported by the Hungarian National Foundation for Scientific Research (OTKA), under grant no. T 7442.  相似文献   

13.
LetX,X 1,X 2,... be i.i.d. random vectors in d. The limit laws that can arise by suitable affine normalizations of the partial sums,S n=X 1+...+X n, are calledoperator-stable laws. These laws are a natural extension to d of the stable laws on. Thegeneralized domain of attraction of [GDOA()] is comprised of all random vectorsX whose partial sums can be affinely normalized to converge to . If the linear part of the affine transformation is restricted to take the formn –B for some exponent operatorB naturally associated to thenX is in thegeneralized domain of normal attraction of [GDONA()]. This paper extends the theory of operator-stable laws and their domains of attraction and normal attraction.  相似文献   

14.
We obtain the asymptotic behaviour for the L norm of the first eigenfunction of the Dirichlet Laplace operator on a conic sector over a geodesic disc in as . We are led to conjecture that for an open, bounded and convex set D with inradius and diameter d, where and   相似文献   

15.
König  H.  Kwapień  S. 《Positivity》2001,5(2):115-152
Let be an i.i.d. sequence of rotationally invariant random vectors in . If X 12 is dominated (in the sense defined below) by Z2 for a rotationally invariant normal random vector Z in , then for each k and
for p3 or p,n2 (resp. for 1p2, n3). The constant ( Zp)1/p is the best possible. The result applies, in particular, for variables uniformly distributed on the sphere S n-1 or the ball B n. In the case of the sphere, the best constant is
With this constant, the Khintchine type inequality in this case also holds for 1p2,n=2.  相似文献   

16.
For an ordinal and a class of topological algebras of a given type (which may be infinite and may contain inflnitary operations), an-aryimplicit operation on is any new-ary operation whose introduction does not eliminate any continuous homomorphisms between members of . The set of all-ary implicit operations on is denoted by and forms an algebra of the given type which is endowed with the least topology making continuous all homomorphisms into members of . With this topology, is a topological algebra in which the subalgebra of all-ary operations on which are induced by terms is dense, provided that is closed under the formation of closed subalgebras and finitary direct products. This is obtained by realizing as an inverse limit of-generated members of . These results are applied to pseudovarieties of topological and finite algebras.This work was supported, in part, by INIC grant 85/CEX/4. This paper was written while the author was a faculty member at the Universidade do Minho.Presented by Ralph McKenzie.  相似文献   

17.
Schep  Anton R. 《Positivity》2003,7(1-2):103-111
Let T be a regular operator from L p L p. Then , where Tr denotes the regular norm of T, i.e., Tr=|T| where |T| denotes the modulus operator of a regular operator T. For p=1 every bounded linear operator is regular and T=Tr, so that the above inequality generalizes the Daugavet equation for operators on L 1–spaces. The main result of this paper (Theorem 9) is a converse of the above result. Let T be a regular linear operator on L p and denote by T A the operator TA. Then for all A with (A)>0 if and only if .  相似文献   

18.
For an arbitrary variety of groups and an arbitrary class of groups that is closed on quotient groups, we prove that a quotient group G/N of the group G possesses an invariant system with - and -factors (respectively, is a residually -group) if G possesses an invariant system with - and -factors (respectively, is a residually -group) and N (respectively, N is a maximal invariant -subgroup of the group G).  相似文献   

19.
For a discrete group G, we prove that a G-map between proper GCW-complexes induces an isomorphism in G-equivariant K-homology if it induces an isomorphism in C-equivariant K-homology for every finite cyclic subgroup C of G. As an application, we show that the source of the Baum–Connes assembly map, namely K * G (E(G, in)), is isomorphic to K * G (E(G, )), where E(G, ) denotes the classifying space for the family of finite cyclic subgroups of G. Letting be the family of virtually cyclic subgroups of G, we also establish that and related results.  相似文献   

20.
Let 1, 2, ... be a sequence of i.i.d. random variables with positive mean and finite variance and letr(b), b0, be real numbers tending to 0 asb . Definings n=1+...+n andS n=Sn(b)=sn+r(b)n, the stopping time =(b)=inf {n>/1:Sn >b} whereb=b(b) , will be considered with special regard to the excess over the boundaryR b=s+r(b)–b. It turns out that the limiting distribution ofR b is the same as in the caser(b)0 for allb. Proving this, Blackwell's renewal theorem and its integral version have to be established first in the above stated situation. Finally, an expansion ofE to vanishing terms asb will be provided and applied to some examples arising in economics.
Zusammenfassung Seien 1, 2, ... unabhängige identisch verteilte Zufallsgrößen mit positivem Erwartungswert und endlicher Varianz sowier(b), b0, reelle Zahlen mitr(b)0 für b. Sei ferners 1, s2, ... der zugehörige Summenprozeß,S n= Sn(b)=sn+r(b)n fürn1 und =(b)=inf {n1: Sn>b, wobeib=b(b) fürb . Es wird gezeigt, daß die asymptotische Verteilung des ExzessesR b=s +r(b)b mit der im Fallr(·)0 übereinstimmt. Dazu werden sowohl das Blackwellsche Erneuerungstheorem als auch seine Integralversion in der vorher beschriebenen parameterabhängigen Situation geeignet formuliert und bewiesen. Als Folgerung ergibt sich dann eine asymptotische Entwicklung vonE(b) fürb bis zu Termen o(1). Anh- and einiger Beispiele aus dem ökonomischen Bereich wird schließlich noch aufgezeigt, wo Approximationen fürE(b) von Interesse sein können.
  相似文献   

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