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1.
In the Hardy Banach spaces H q , Bergman Banach spaces Hq, and Banach spaces (p, q, ), we determine the exact values of the Kolmogorov, Bernstein, Gelfand, linear, and trigonometric n-widths of classes of functions analytic in the disk |z| < 1 and such that the averaged moduli of continuity of their r-derivatives are majorized by a certain function. For these classes, we also consider the problems of optimal recovery and coding of functions.__________Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 9, pp. 1155–1171, September, 2004.  相似文献   

2.
Two-parameter Vilenkin systems will be investigated. First we give a general sufficient condition for multipliers to be bounded between two-dimensional Hardy spaces H q(0<q1). By means of interpolation and duality argument, this theorem can be extended to other spaces. As a consequence, we can prove the (H q , L q)-boundedness of the Sunouchi operator U with respect to two-parameter Vilenkin systems for all 0 <q 1. Moreover, the equivalence f{Hq} ~ Ufq (f Hq)follows for 1/2<q 1.  相似文献   

3.
, , . . . [1], , . , , ., , L logL. , , . . . . [5]. , .  相似文献   

4.
In an attempt to find a q-analogue of Weber and Schafheitlin's integral 0 x J (ax) J (bx) dx which is discontinuous on the diagonal a = b the integral 0 x J (2) (a(1 – q)x; q)J (1) (b(1 – q)x; q) dx is evaluated where J (1) (x; q) and J (2) (x; q) are two of Jackson's three q-Bessel functions. It is found that the question of discontinuity becomes irrelevant in this case. Evaluations of this integral are also made in some interesting special cases. A biorthogonality formula is found as well as a Neumann series expansion for x in terms of J (2) +1+2n ((1 – q)x; q). Finally, a q-Lommel function is introduced.  相似文献   

5.
LetG be a compact group of automorphism acting continuously on a compact groupH. Then the orbit spaceH G is a compact hypergroup. We characterize, all solvable groupsH and compact automorphism groupsG for whichH G is almost discrete, i.e.,H G is homeomorphic to the one-point-compactification of . It turns out that thenH is isomorphic either to the infinite direct product (p) of the cyclic groups (p) or to p n ( p the group of allp-adic numbers) for some primep and some . The almost discrete orbit hypergroupsH G are determined explicitly for some examples.  相似文献   

6.
The fundamental result: if and v are two finite Borel measures, defined in the spaceL p[0, 1] (1p<) or in C(K) (K is a metric compactum without isolated points), then from the equalities (B)=v(B) for all balls B of radius 1 there follows that =v. In addition, in the spaces C(K) and p (1p<) from the inequalities (B) v(B) there follows that v.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 177, pp. 122–128, 1989.  相似文献   

7.
This paper is concerned with the existence and boundedness of the solutions to the linear complementarity problemw=Mz+q,w0,z0,w T z=0, for eachq n . It has been previously established that, ifM is copositive plus, then the solution set is nonempty and bounded for eachq n iffM is aQ-matrix. This result is shown to be valid also forL 2-matrices,P 0-matrices, nonnegative matrices, andZ-matrices.  相似文献   

8.
Vakarchuk  S. B. 《Mathematical Notes》2002,72(5-6):615-619
In the Hardy space H p, (p1, 0< 1, H p,1 H p) we develop best linear approximation methods (previously studied by Taikov and Ainulloev) for the classes W(r,,) of analytic functions on the unit disk and calculate the exact values of linear, Gelfand, and informational n-widths of these classes.  相似文献   

9.
Summary We say that the discD()R 2, of radius , located around the origin isp-covered in timeT by a Wiener processW(·) if for anyzD() there exists a 0tT such thatW(t) is a point of the disc of radiusp, located aroundz. The supremum of those 's (0) is studied for which,D() isp-covered inT.  相似文献   

10.
The first part of this paper describes the construction of pseudo-Riemannian homogeneous spaces with special curvature properties such as Einstein spaces, using corresponding known compact Riemannian ones. This construction is based on the notion of a certain duality between compact and non-compact homogeneous spaces. In the second part we apply this method to obtain pseudo-Riemannian homogeneous manifolds with real Killing spinors. We will prove that under a certain additional condition a dual pseudo-Riemannian space (G/H, g) of a compact Riemannian homogeneous space (G/H, g) with homogeneousSpin-structure admits a homogeneousSpin +-structure and theG_invariant Killing spinors on (G/H, g) correspond toG-invariant Killing spinors on (G/H, g). We can ensure that in most cases the hypothesis onG-invariance is satisfied.  相似文献   

11.
Let s 0 and let + s be the set of functions x defined on a finite interval I and such that, for all collections of s + 1 pairwise different points t 0,..., t s I, the corresponding divided differences [x; t 0,...,t s ] of order s are nonnegative. Let + s B p + s B p, 1 p where B p is a unit ball in the space L p, and let + s L q + s L q, 1 q . For every s 3 and 1 q p , we determine the exact orders of the shape-preserving Kolmogorov widths {x - y} \right\ L_q , $$]]>, where M n is the collection of all affine linear manifolds M n in L q such that dim M n n and M n + s L q .Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 7, pp. 901–926, July, 2004.  相似文献   

12.
A new construction is given for difference matrices. The generalized Hadamard matrices GH(q(q – 1)2; EA(q)) are constructed whenq andq – 1 are both prime powers. Other generalised Hadamard matrices are also shown to exist. For example, there exist GH(n; G) forn = 52 2 3, 26 32, 112 22 3, 172 2 32, 532 2 33, 712 22 32, 1072 22 33, 1492 52 2 3,.... Finally, a new construction for the BGW ((q 4 – 1)/(q – 1),q 3,q 2(q – 1);q q-1), and a construction for the new BGW ((q 8 – 1)/(q 2 – 1),q 6,q 4(q 2 – 1);G) are given, wheneverq is a prime power, andG is a group of orderq + 1.  相似文献   

13.
For 0<1 and graphsG andH, we writeGH if any -proportion of the edges ofG span at least one copy ofH inG. As customary, we writeC k for a cycle of lengthk. We show that, for every fixed integerl1 and real >0, there exists a real constantC=C(l, ), such that almost every random graphG n, p withp=p(n)Cn –1+1/2l satisfiesG n,p1/2+ C 2l+1. In particular, for any fixedl1 and >0, this result implies the existence of very sparse graphsG withG 1/2+ C 2l+1.The first author was partially supported by NSERC. The second author was partially supported by FAPESP (Proc. 93/0603-1) and by CNPq (Proc. 300334/93-1). The third author was partially sopported by KBN grant 2 1087 91 01.  相似文献   

14.
We consider measurable subsets {ofR}n with 0<m()<, and we assume that has a spectral set . (In the special case when is also assumed open, may be obtained as the joint spectrum of a family of commuting self-adjoint operators {H k: 1kn} in L 2 () such that each H k is an extension of i(/x k) on C c (), k=1, ..., n.)It is known that is a fundamental domain for a lattice if is itself a lattice. In this paper, we consider a class of examples where is not assumed to be a lattice. Instead is assumed to have a certain inhomogeneous form, and we prove a necessary and sufficient condition for to be a fundamental domain for some lattice in {ofR}n. We are thus able to decide the question, fundamental domain or not, by considering only properties of the spectrum . Our criterion is obtained as a corollary to a theorem concerning partitions of sets which have a spectrum of inhomogeneous form.Work supported in part by the NSF.Work supported in part by the NSRC, Denmark.  相似文献   

15.
If (P, L) is a projective plane and is a triangle presentation compatible with a point-line correspondence :P L, then gives rise to a group and a thick building of typeà 2 on the vertices of which acts simply transitively. We find all triangle presentations (up to natural equivalence) compatible with some point-line correspondence :P L, when (P, L) is the projective plane of orderq=2 orq=3. For some, but not all, of these , is isomorphic to the building associated withG=PGL(3,K) whereK is a local field with discrete valuation and residual field of orderq. We identify the for which this is the case, and in these cases, find embeddings of intoG. We also describe the arithmetic nature of these groups.  相似文献   

16.
This paper is concerned with the arithmetic of curves of the form vp=us(1-u), where p is a prime with p 5 and s is an integer such that 1 s p-2. The Jacobians of these curves admit complex multiplication by a primitive p-th root of unity . We find explicit rational functions on these curves whose divisors are p-multiples of divisors representing (1-)2 - and (1-)3-division points on the corresponding Jacobians. This also gives an effective version of a theorem of Greenberg.  相似文献   

17.
Summary The existence of optimal nodes with preassigned multiplicities is proved for the Hardy spacesH p (1<p<). This is then used to show that the exact order of convergence for the optimal qudrature formula withN nodes (including multiplicity) is where 1/p+1/q=1 and 1p.  相似文献   

18.
A strong law for weighted sums of i.i.d. random variables   总被引:4,自引:0,他引:4  
A strong law is proved for weighted sumsS n=a in X i whereX i are i.i.d. and {a in} is an array of constants. When sup(n –1|a in | q )1/q <, 1<q andX i are mean zero, we showE|X| p <,p l+q –1=1 impliesS n /n 0. Whenq= this reduces to a result of Choi and Sung who showed that when the {a in} are uniformly bounded,EX=0 andE|X|< impliesS n /n 0. The result is also true whenq=1 under the additional assumption that lim sup |a in |n –1 logn=0. Extensions to more general normalizing sequences are also given. In particular we show that when the {a in} are uniformly bounded,E|X|1/< impliesS n /n 0 for >1, but this is not true in general for 1/2<<1, even when theX i are symmetric. In that case the additional assumption that (x 1/ log1/–1 x)P(|X|x)0 asx provides necessary and sufficient conditions for this to hold for all (fixed) uniformly bounded arrays {a in}.  相似文献   

19.
LetA(·) be ann × n symmetric affine matrix-valued function of a parameteruR m , and let (u) be the greatest eigenvalue ofA(u). Recently, there has been interest in calculating (u), the subdifferential of atu, which is useful for both the construction of efficient algorithms for the minimization of (u) and the sensitivity analysis of (u), namely, the perturbation theory of (u). In this paper, more generally, we investigate the Legendre-Fenchel conjugate function of (·) and the -subdifferential (u) of atu. Then, we discuss relations between the set (u) and some perturbation bounds for (u).The author is deeply indebted to Professor J. B. Hiriart-Urruty who suggested this study and provided helpful advice and constant encouragement. The author also thanks the referees and the editors for their substantial help in the improvement of this paper.  相似文献   

20.
Summary In this paper we establish a large deviations principle for the invariant measure of the non-Gaussian stochastic partial differential equation (SPDE) t v =v +f(x,v )+(x,v ) . Here is a strongly-elliptic second-order operator with constant coefficients, h:=DH xx-h, and the space variablex takes values on the unit circleS 1. The functionsf and are of sufficient regularity to ensure existence and uniqueness of a solution of the stochastic PDE, and in particular we require that 0<mM wherem andM are some finite positive constants. The perturbationW is a Brownian sheet. It is well-known that under some simple assumptions, the solutionv 2 is aC k (S 1)-valued Markov process for each 0<1/2, whereC (S 1) is the Banach space of real-valued continuous functions onS 1 which are Hölder-continuous of exponent . We prove, under some further natural assumptions onf and which imply that the zero element ofC (S 1) is a globally exponentially stable critical point of the unperturbed equation t 0 = 0 +f(x,0), that has a unique stationary distributionv K, on (C (S 1), (C K (S 1))) when the perturbation parameter is small enough. Some further calculations show that as tends to zero,v K, tends tov K,0, the point mass centered on the zero element ofC (S 1). The main goal of this paper is to show that in factv K, is governed by a large deviations principle (LDP). Our starting point in establishing the LDP forv K, is the LDP for the process , which has been shown in an earlier paper. Our methods of deriving the LDP forv K, based on the LDP for are slightly non-standard compared to the corresponding proofs for finite-dimensional stochastic differential equations, since the state spaceC (S 1) is inherently infinite-dimensional.This work was performed while the author was with the Department of Mathematics, University of Maryland, College Park, MD 20742, USA  相似文献   

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