共查询到20条相似文献,搜索用时 31 毫秒
1.
Let μ be a real measure on the line such that its Poisson integral M(z) converges and satisfies|M(x+iy)|Ae−cyα, y→+∞,for some constants A,c>0 and 0<α1. We show that for 1/2<α1 the measure μ must have many sign changes on both positive and negative rays. For 0<α1/2 this is true for at least one of the rays, and not always true for both rays. Asymptotical bounds for the number of sign changes are given which are sharp in some sense. 相似文献
2.
A finite group G is called an ah-group if any two distinct conjugacy classes of G have distinct cardinality. We show that if G is an ah-group, then the non-abelian socle of G is isomorphic to one of the following:
- 1. , for 1a5, a≠2.
- 2. A8.
- 3. PSL(3,4)e, for 1e10.
- 4. A5×PSL(3,4)e, for 1e10.
- 1. , for 3a5.
- 2. PSL(3,4)e, for 1e10.
3.
4.
In this paper we present some new results about unlike powers in arithmetic progression. We prove among other things that for given k 4 and L 3 there are only finitely many arithmetic progressions of the form with xi , gcd(x0, xl) = 1 and 2 li L for i = 0, 1, …, k − 1. Furthermore, we show that, for L = 3, the progression (1, 1,…, 1) is the only such progression up to sign. Our proofs involve some well-known theorems of Faltings [9], Darmon and Granville [6] as well as Chabauty's method applied to superelliptic curves. 相似文献
5.
The continuity conditions at the endpoints of interpolation theorems, TaBjMj aAj for j=0, 1, can be written with the help of the approximation functional: E(t, Ta; B1, B0)L∞M0 aA0 and E(t, Ta; B0, B1)L∞M1 aA1. As a special case of the results we present here we show that in the hypotheses of the interpolation theorem the L∞ norms can be replaced by BMO(
+) norms. This leads to a strong version of the Stein-Weiss theorem on interpolation with change of measure. Another application of our results is that the condition fL0, i.e., f*L∞, where f*(γ)=μ{|f|>γ} is the distribution function of f, can be replaced in interpolation with L(p, q) spaces by the weaker f*BMO(
+). 相似文献
6.
Javad Namazi 《Journal of Mathematical Analysis and Applications》2004,290(2):553-562
Let 1<p<∞, and k,m be positive integers such that 0(k−2m)pn. Suppose ΩRn is an open set, and Δ is the Laplacian operator. We will show that there is a sequence of positive constants cj such that for every f in the Sobolev space Wk,p(Ω), for all xΩ except on a set whose Bessel capacity Bk−2m,p is zero. 相似文献
7.
Victor H. de la Pea Rustam Ibragimov Shaturgun Sharakhmetov 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2002,38(6):973
In this paper, we present a method that allows one to obtain a number of sharp inequalities for expectations of functions of infinite-degree U-statistics. Using the approach, we prove, in particular, the following result: Let D be the class of functions f :R+→R+ such that the function f(x+z)−f(x) is concave in xR+ for all zR+. Then the following estimate holds: for all fD and all U-statistics ∑1i1<<ilnYi1,…,il(Xi1,…,Xil) with nonnegative kernels Yi1,…,il :Rl→R+, 1ikn; ir≠is, r≠s; k,r,s=1,…,l; l=0,…,m, in independent r.v.'s X1,…,Xn. Similar inequality holds for sums of decoupled U-statistics. The class D is quite wide and includes all nonnegative twice differentiable functions f such that the function f″(x) is nonincreasing in x>0, and, in particular, the power functions f(x)=xt, 1<t2; the power functions multiplied by logarithm f(x)= (x+x0)t ln(x+x0), 1<t<2, x0max(e(3t2−6t+2)/(t(t−1)(2−t)),1); and the entropy-type functions f(x)=(x+x0)ln(x+x0), x01. As an application of the results, we determine the best constants in Burkholder–Rosenthal-type inequalities for sums of U-statistics and prove new decoupling inequalities for those objects. The results obtained in the paper are, to our knowledge, the first known results on the best constants in sharp moment estimates for U-statistics of a general type. 相似文献
8.
Suppose that G is a graph with n vertices and m edges, and let μ be the spectral radius of its adjacency matrix.Recently we showed that if G has no 4-cycle, then μ2-μn-1, with equality if and only if G is the friendship graph.Here we prove that if m9 and G has no 4-cycle, then μ2m, with equality if G is a star. For 4m8 this assertion fails. 相似文献
9.
Vladimir I. Bogachev Nicolai V. Krylov Michael Rckner 《Journal de Mathématiques Pures et Appliquées》2006,85(6):743-757
We consider elliptic equations of the form L*μ=ν for measures on . The membership of solutions in the Sobolev classes is established under appropriate conditions on the coefficients of L. Bounds of the form (x)CΦ(x)−1 for the corresponding densities are obtained. 相似文献
10.
11.
Let I be a finite interval, , and 1p∞. Given a set M, of functions defined on I, denote by the subset of all functions yM such that the s-difference is nonnegative on I, τ>0. Further, denote by the Sobolev class of functions x on I with the seminorm x(r)Lp1. We obtain the exact orders of the Kolmogorov and the linear widths, and of the shape-preserving widths of the classes in Lq for s>r+1 and (r,p,q)≠(1,1,∞). We show that while the widths of the classes depend in an essential way on the parameter s, which characterizes the shape of functions, the shape-preserving widths of these classes remain asymptotically ≈n-2. 相似文献
12.
Alexandre Junod 《Expositiones Mathematicae》2003,21(1):63
We develop a general context for the computation of the determinant of a Hankel matrix Hn = (αi+j)0i,jn, assuming some suitable conditions for the exponential (or ordinary) generating function of the sequence (αn)n0. Several well-known particular cases are thus derived in a unified way. 相似文献
13.
Andrs Kro 《Journal of Approximation Theory》2001,111(2):303
Let K be a convex body in
d (d2), and denote by Bn(K) the set of all polynomials pn in
d of total degree n such that |pn|1 on K. In this paper we consider the following question: does there exist a p*nBn(K) which majorates every element of Bn(K) outside of K? In other words can we find a minimal γ1 and p*nBn(K) so that |pn(x)|γ |p*n(x)| for every pnBn(K) and x
d\K? We discuss the magnitude of γ and construct the universal majorants p*n for evenn. It is shown that γ can be 1 only on ellipsoids. Moreover, γ=O(1) on polytopes and has at most polynomial growth with respect to n, in general, for every convex body K. 相似文献
14.
We consider boolean circuits C over the basis Ω={,} with inputs x1, x2,…,xn for which arrival times are given. For 1in we define the delay of xi in C as the sum of ti and the number of gates on a longest directed path in C starting at xi. The delay of C is defined as the maximum delay of an input.Given a function of the form
f(x1,x2,…,xn)=gn−1(gn−2(…g3(g2(g1(x1,x2),x3),x4)…,xn−1),xn)