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1.
Let (E, ¦·¦) be a uniformly convex Banach space with the modulus of uniform convexity of power type. Let be the convolution of the distribution of a random series inE with independent one-dimensional components and an arbitrary probability measure onE. Under some assumptions about the components and the smoothness of the norm we show that there exists a constant such that |{·<t}–{·+r<t}|r q , whereq depends on the properties of the norm. We specify it in the case ofL spaces, >1.  相似文献   

2.
We prove a local limit theorem (LLT) on Cramer-type large deviations for sums S V = t V ( t ), where t , t Z , 1, is a Markov Gaussian random field, V Z , and is a bounded Borel function. We get an estimate from below for the variance of S V and construct two classes of functions , for which the LLT of large deviations holds.  相似文献   

3.
Leta be irrational and letf:[0,1] be Riemann-integrable with integral zero. Letf n (x) denote the Weyl sumf n (x):= k=0 n–1 f({x k>}),x/[0,1[,n. We prove criteria for the boundedness of the sequence (f n ) n1 and discuss the relation of this question to irregularities of the distribution of sequences.  相似文献   

4.
, (t) >0 E(–, +),E<, , ¦f(t(t) xE, f(t)=0 (–, +).  相似文献   

5.
Résumé Certaines méthodes directes et indirectes pour le calcul de Max {x t Ax, (x)1} sont étudiées.Les méthodes directes sont basées sur les propriétés particulières des normes 1, 2 et . Ces méthodes sont très simples mais ne s'appliquent qu'à certaines familles de matrices.La méthode indirecte est la méthode autoduale introduite dans [25, 26] avec = 1. Dans ce cas, le choix du vecteur initial pour qu'il y ait convergence vers une solution optimale est largement discuté.
Some methods for computing the maximum of quadratic from on the unit ball of the maximum norm
Summary Some direct and indirect methods are studied for computing Max {x t Ax, (x)1} whereA is symmetric definite positive.Direct methods are constructed using particular properties of 1, 2, norms. These methods are very simple, but uniquely suitable to certains families of matrices.The indirect method is the autodual method, introduced in [25, 26, 29] with = 1. In this case the problem of choosing an initial vector so that convergence of the iterative sequence occurs to an optimal solution is largely discussed.
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6.
For any stable distribution on the line, recurrence-transience of the selfsimilar additive process {X t ,t0} with (X 1)= is determined. Comparison with the stable Lévy process {Y t ,t0} with (Y 1)= is made: if is not strictly stable, then {Y t } is transient but {X t } is recurrent except the obviously transient case of monotone sample functions.  相似文献   

7.
Given a Young function , we study the existence of copies of c 0 and in cabv (,X) and in cabsv (,X), the countably additive, -continuous, and X-valued measure spaces of bounded -variation and bounded -semivariation, respectively.  相似文献   

8.
Let X n1 * , ... X nn * be a sequence of n independent random variables which have a geometric distribution with the parameter p n = 1/n, and M n * = \max\{X n1 * , ... X nn * }. Let Z 1, Z2, Z3, ... be a sequence of independent random variables with the uniform distribution over the set N n = {1, 2, ... n}. For each j N n let us denote X nj = min{k : Zk = j}, M n = max{Xn1, ... Xnn}, and let S n be the 2nd largest among X n1, Xn2, ... Xnn. Using the methodology of verifying D(un) and D'(un) mixing conditions we prove herein that the maximum M n has the same type I limiting distribution as the maximum M n * and estimate the rate of convergence. The limiting bivariate distribution of (Sn, Mn) is also obtained. Let n, n Nn, , and T n = min{M(An), M(Bn)}. We determine herein the limiting distribution of random variable T n in the case n , n/n > 0, as n .  相似文献   

9.
We study (set-valued) mappings of bounded -variation defined on the compact interval I and taking values in metric or normed linear spaces X. We prove a new structural theorem for these mappings and extend Medvedev's criterion from real valued functions onto mappings with values in a reflexive Banach space, which permits us to establish an explicit integral formula for the -variation of a metric space valued mapping. We show that the linear span GV (I;X) of the set of all mappings of bounded -variation is automatically a Banach algebra provided X is a Banach algebra. If h:I× X Y is a given mapping and the composition operator is defined by (f)(t)=h(t,f(t)), where tI and f:I X, we show that :GV (I;X) GV (I;Y) is Lipschitzian if and only if h(t,x)=h0(t)+h1(t)x, tI, xX. This result is further extended to multivalued composition operators with values compact convex sets. We prove that any (not necessarily convex valued) multifunction of bounded -variation with respect to the Hausdorff metric, whose graph is compact, admits regular selections of bounded -variation.  相似文献   

10.
Liskevich  Vitali  Sobol  Zeev 《Potential Analysis》2003,18(4):359-390
In this paper we obtain pointwise two-sided estimates for the integral kernel of the semigroup associated with second-order elliptic differential operators –(a)+b 1+b 2+V with real measurable (singular) coefficients, on an open set R N . The assumptions we impose on the lower-order terms allow for the case when the semigroup exists on L p () for p only from an interval in [1,), neither enjoys a standard Gaussian estimate nor is ultracontractive in the scale L p (). We show however that the semigroup is ultracontractive in the scale of weighted spaces L p (,2dx) with a suitable weight and derive an upper and lower bound on its integral kernel.  相似文献   

11.
12.
Let t be the flow (parametrized with respect to arc length) of a smooth unit vector field v on a closed Riemannian manifold M n , whose orbits are geodesics. Then the (n-1)-plane field normal to v, v, is invariant under d t and, for each x M, we define a smooth real function x (t) : (1 + i (t)), where the i(t) are the eigenvalues of AA T, A being the matrix (with respect to orthonormal bases) of the non-singular linear map d2t , restricted to v at the point x -t M n.Among other things, we prove the Theorem (Theorem II, below). Assume v is also volume preserving and that x ' (t) 0 for all x M and real t; then, if x t : M M is weakly missng for some t, it is necessary that vx 0 at all x M.  相似文献   

13.
Let A and B be normal matrices. In :={x=(xk) ¦ xk} we define the order relation A by xA0:<=> k=0 n ankxk0 (n ). Let T be a row-finite matrix. A is called T-section-positive, if ktmkxke(k) A0 (m ) for xA0 (see [5]). We study the relation between T-sectional positivity and T-sectional boundedness. An (A,B)-summability factor sequence =(k) is called positive, if (kxk)B0 for each xcA with xA0. For B-section-positive matrices A we give a functional analytic characterization of positive (A,B)-summability factor sequences.

Die Arbeit entstand während eines vom DAAD unterstützten Forschungsaufenthalts an der Fernuniversität-Gesamthochschule Hagen  相似文献   

14.
We give a classification of 3—dimensional conformally flat contact metric manifolds satisfying: =0(=L g) orR(Y, Z)=k[(Z)Y–(Y)Z]+[(Z)hY]–(Y)hZ] wherek and are functions. It is proved that they are flat (the non-Sasakian case) or of constant curvature 1 (the Sasakian case).  相似文献   

15.
Let (n) be a system, close to the orthonormal complete system (x n). An estimate is obtained for the deviation of the system {fn}, obtained from {n} by Schmidt's method, from the system {xn}. This estimate is used to show that, in any LP(–1,1), withp (1,4/3] [4,), and for any >e¦4 = i,13..., there exists an orthogonal algebraic system (P n (x)) n=0 , forming a basis in LP and such that n = degP n (x) n for n>no(p,).Translated from Matematicheskie Zametki, Vol. 23, No. 2, pp. 223–230, February, 1978.  相似文献   

16.
We study the problem of finding constant mean curvature graphsover a domain of a totally geodesic hyperplane andan equidistant hypersurface Q of hyperbolic space. We findthe existence of graphs of constant mean curvature H overmean convex domains Q and with boundary for –H < H |h|, where H > 0 is the mean curvature of the boundary . Here h is the mean curvature respectively of the geodesic hyperplane (h= 0) and of the equidistant hypersurface (0 < |h|< 1). The lower bound on H is optimal.  相似文献   

17.
A stochastic model of an epidemic is investigated, taking account of the removal of ill members of the population (by death, by recovery with immunization, by isolation) and natural immunization. Limiting distributions are found for the size of the epidemic, the number immunized 1, and their sum, under the assumption that the original number of susceptible individuals n and the number of ill individuals m , while n 1,n 0< , where and are the coefficients for the contraction of the disease and of immunization respectively.Translated from Matematicheskie Zametki, Vol. 8, No. 3, pp. 385–392, September, 1970.  相似文献   

18.
We consider the set of regular functions . We construct a Borel measure and a class of outer measures h onH. With these and h we show that: (HS)=0 and h (HS)=0, (S is the set of normed univalent functions). From h (HS)=0 follows—forh=t —that the Hausdorff—Billingsley-dimension ofHS is zero.  相似文献   

19.
We study the class of bounded C 0-semigroups T=(T t ) t0 on a Banach space X satisfying the asymptotic finite dimensionality condition: codim X 0(T)<, where X 0(T):={x X:limt T t x=0}. We prove a theorem which provides some necessary and sufficient conditions for asymptotic finite dimensionality.  相似文献   

20.
Moser-type estimates for functions whose gradient is in the Lorentz space L(n, q), 1q, are given. Similar results are obtained for solutions uH inf0 sup1 of Au=(f i ) x i , where A is a linear elliptic second order differential operator and |f|L(n, q), 2q.Work partially supported by MURST (40%).  相似文献   

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