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991.
Zhizhiashvili studied questions associated with the approximation properties of Cesàro means of trigonometric Fourier series for functions of two variables in the spaces H. It is proved here that the corresponding estimate cannot be improved for p = 1 or p = . 相似文献
992.
Suppose that
is an arbitrary finite complex Borel measure on the interval
is its Poisson integral,
and
are the conjugate harmonics of
, and
is the nontangential limiting value of the analytic function
as
. In this paper, we consider the problem of representing the analytic function
in terms of its boundary values
. 相似文献
993.
Suppose that k and l are integers such that
and
, M
k is a set of numbers without kth powers, and
. In this paper, we obtain asymptotic estimates of the sums
over
相似文献
994.
Let
be a sequence of complex numbers such that
as
. For
close to the imaginary axis, upper bounds of the indicator of a nonzero entire function of exponential type with minimal growth vanishing on
is obtained. These bounds give sufficient conditions for the system of exponents
to be incomplete in an unbounded domain in
. 相似文献
995.
In this paper, we generalize Bernstein's theorem characterizing the space
by means of local approximations. The closed interval
is partitioned into disjoint half-intervals on which best approximation polynomials of degree
divided by the lengths of these half-intervals taken to the power
are considered. The existence of the limits of these ratios as the lengths of the half-intervals tend to zero is a criterion for the existence of the
th derivative of a function. We prove the theorem in a stronger form and extend it to the spaces
. 相似文献
996.
Let X and Y be Banach spaces and ψ a continuous convex function on the unit interval [0,1] satisfying certain conditions. Let X⊕ψY be the direct sum of X and Y equipped with the associated norm with ψ. We show that X⊕ψY is uniformly convex if and only if X,Y are uniformly convex and ψ is strictly convex. As a corollary we obtain that the ?p,q-direct sum (not p=q=1 nor ∞), is uniformly convex if and only if X,Y are, where ?p,q is the Lorentz sequence space. These results extend the well-known fact for the ?p-sum . Some other examples are also presented. 相似文献
997.
Sanghyun Cho 《Journal of Mathematical Analysis and Applications》2003,283(2):386-397
Let Ω be a smoothly bounded pseudoconvex domain in and let be a point of finite type. We also assume that the Levi form of bΩ is comparable in a neighborhood of z0. Then we get a quantity which bounds from above and below the Bergman kernel function in a small constant and large constant sense. 相似文献
998.
Endre Boros Khaled Elbassioni Vladimir Gurvich Leonid Khachiyan 《Mathematical Programming》2003,98(1-3):355-368
A result of Balas and Yu (1989) states that the number of maximal independent sets of a graph G is at most p+1, where is the number of pairs of vertices in G at distance 2, and p is the cardinality of a maximum induced matching in G. In this paper, we give an analogue of this result for hypergraphs and, more generally, for subsets of vectors in the product of n lattices =1××n, where the notion of an induced matching in G is replaced by a certain binary tree each internal node of which is mapped into . We show that our bounds may be nearly sharp for arbitrarily large hypergraphs and lattices. As an application, we prove that the number of maximal infeasible vectors x=1××n for a system of polymatroid inequalities does not exceed max{Q,logt/c(2Q,)}, where is the number of minimal feasible vectors for the system, , , and c(,) is the unique positive root of the equation 2c(c/log–1)=1. This bound is nearly sharp for the Boolean case ={0,1}n, and it allows for the efficient generation of all minimal feasible sets to a given system of polymatroid inequalities with quasi-polynomially bounded right-hand sides .
This research was supported by the National Science Foundation (Grant IIS-0118635), and by the Office of Naval Research (Grant N00014-92-J-1375). The second and third authors are also grateful for the partial support by DIMACS, the National Science Foundation's Center for Discrete Mathematics and Theoretical Computer Science.Mathematics Subject Classification (2000):20E28, 20G40, 20C20 相似文献
999.
Włodzimierz Bryc 《Journal of Theoretical Probability》2003,16(4):935-955
We prove the large deviation principle for the joint empirical measure of pairs of random variables which are coupled by a totally symmetric interaction. The rate function is given by an explicit bilinear expression, which is finite only on product measures and hence is non-convex. 相似文献
1000.