共查询到20条相似文献,搜索用时 46 毫秒
1.
The nth cyclic function is defined by
We prove that if k is an integer with 1kn−1, then
holds for all positive real numbers x with the best possible constantsα=1 and β= 2n-k over n. 相似文献
Full-size image
Full-size image
2.
A. Bultheel P. González-Vera E. Hendriksen O. Njåstad 《Journal of Approximation Theory》1997,89(3):344-371
In Akhiezer's book [“The Classical Moment Problem and Some Related Questions in Analysis,” Oliver & Boyd, Edinburghasol;London, 1965] the uniqueness of the solution of the Hamburger moment problem, if a solution exists, is related to a theory of nested disks in the complex plane. The purpose of the present paper is to develop a similar nested disk theory for a moment problem that arises in the study of certain orthogonal rational functions. Let {αn}∞n=0be a sequence in the open unit disk in the complex plane, let
(
/|αk|=−1 whenαk=0), and let
We consider the following “moment” problem: Given a positive-definite Hermitian inner product ·, · on
×
, find a non-decreasing functionμon [−π, π] (or a positive Borel measureμon [−π,π)) such that
In particular we give necessary and sufficient conditions for the uniqueness of the solution in the case that
If this series diverges the solution is always unique. 相似文献
Full-size image
Full-size image
Full-size image
3.
Yildiray Ozan 《Journal of Pure and Applied Algebra》2002,170(2-3)
Assume that X is a compact connected orientable nonsingular real algebraic variety with an algebraic free S1-action so that the quotient Y=X/S1 is also a real algebraic variety. If π : X→Y is the quotient map then the induced map between reduced algebraic K-groups, tensored with
,
is onto, where
,
denoting the ring of entire rational (regular) functions on the real algebraic variety X, extending partially the Bochnak–Kucharz result that
for any real algebraic variety X. As an application we will show that for a compact connected Lie group G
. 相似文献
Full-size image
Full-size image
4.
Let the function fC[0,1] satisfy f(
. We prove the estimate
. 相似文献
Full-size image
5.
Oblique Projections and Abstract Splines 总被引:1,自引:0,他引:1
Given a closed subspace
of a Hilbert space
and a bounded linear operator AL(
) which is positive, consider the set of all A-self-adjoint projections onto
:
In addition, if
1 is another Hilbert space, T:
→
1 is a bounded linear operator such that T*T=A and ξ
, consider the set of (T,
) spline interpolants to ξ:
A strong relationship exists between
(A,
) and sp(T,
,ξ). In fact,
(A,
) is not empty if and only if s p(T,
,ξ) is not empty for every ξ
. In this case, for any ξ
it holds
and for any ξ
, the unique vector of s p(T,
,ξ) with minimal norm is (1−PA,
)ξ, where PA,
is a distinguished element of
(A,
). These results offer a generalization to arbitrary operators of several theorems by de Boor, Atteia, Sard and others, which hold for closed range operators. 相似文献
Full-size image
Full-size image
Full-size image
6.
Jos M. Rodríguez 《Journal of Approximation Theory》2001,108(2):119
We characterize the set of functions which can be approximated by polynomials with the following norm
for a big class of weights w0, w1, …, wk 相似文献
Full-size image
7.
The object of this paper is to study the rapidity of convergence of the Taylor mean of the Fourier series of ƒ(x) when ƒ(x) belongs to the class Lip(α, p). We show that it is of Jackson order provided that a suitable integrability condition is imposed upon the function
. 相似文献
Full-size image
8.
We present an upper bound for the ratio [formula], where f is a positive decreasing function satisfying
for all t (0, a]. Our result sharpens an inequality of L. Nania. 相似文献
Full-size image
9.
Partially dynamic maintenance of minimum weight hyperpaths 总被引:1,自引:0,他引:1
Giorgio Ausiello Paolo Giulio Franciosa Daniele Frigioni 《Journal of Discrete Algorithms》2005,3(1):27-46
We address the problem of dynamically maintaining minimum weight hyperpaths in a directed hypergraph in a decremental setting. For such a problem, we provide a new efficient algorithm that works for a wide class of hyperpath weight measures. This algorithm explicitly updates minimum weight hyperpaths in
worst case time under a sequence of L hyperarc weight increments and hyperarc deletions, where C is the maximum weight of minimum hyperpaths in
and
is the size of the representation of the hypergraph. Hyperpath weight measures are only required to belong to the class of strict weakly superior functions. 相似文献
Full-size image
10.
Michael I. Ganzburg 《Journal of Approximation Theory》2002,119(2):193-213
In this paper, we establish new asymptotic relations for the errors of approximation in Lp[−1,1], 0<p∞, of xλ, λ>0, by the Lagrange interpolation polynomials at the Chebyshev nodes of the first and second kind. As a corollary, we show that the Bernstein constant
is finite for λ>0 and
. 相似文献
Full-size image
11.
U. an der Heiden 《Journal of Mathematical Analysis and Applications》1979,70(2):599-609
It is proved that the autonomous difference-differential equation
(0) has, for a broad class of functions f, a nonconstant periodic solution whenever the associated characteristic equation has a root with positive real part. 相似文献
Full-size image
12.
Precise asymptotics in some strong limit theorems for multidimensionally indexed random variables 总被引:1,自引:0,他引:1
Consider Z+d (d2)—the positive d-dimensional lattice points with partial ordering , let {Xk,kZ+d} be i.i.d. random variables with mean 0, and set Sn=∑knXk, nZ+d. We establish precise asymptotics for ∑n|n|r/p−2P(|Sn||n|1/p), and for
, (0δ1) as 0, and for
as
. 相似文献
Full-size image
Full-size image
13.
Let p > 1, and dμ a positive finite Borel measure on the unit circle Γ: = {z ε C: ¦z¦ = 1}. Define the monic polynomial φn, p(z)=zn+…εPn >(the set of polynomials of degree at most n) satisfying
. Under certain conditions on dμ, the asymptotics of φn, p(z) for z outside, on, or inside Γ are obtained (cf. Theorems 2.2 and 2.4). Zero distributions of φn, p are also discussed (cf. Theorems 3.1 and 3.2). 相似文献
Full-size image
14.
Wolfgang Luh Valeri A. Martirosian Jürgen Müller 《Journal of Approximation Theory》2002,114(2):201-213
We prove the existence of a function which is holomorphic exactly in the unit disk
and has universal translates with respect to a prescribed closed set E∂
and satisfies C∞(∂
\E). If Q is a subsequence of
0 with upper density d(Q)=1 then the function can be constructed such that in addition
相似文献
Full-size image
15.
Generalizations of prophet inequalities for single sequences are obtained for optimal stopping of several parallel sequences of independent random variables. For example, if {Xi, j, 1 ≤ i ≤ n, 1 ≤ j < ∞} are independent non-negative random variables, then
and this bound is best possible. Applications are made to comparisons of the optimal expected returns of various alternative methods of stopping of parallel processes. 相似文献
Full-size image
16.
We prove the existence of homogeneous target pattern and spiral solutions to equations of the form
; the spatial dimension is greater than one. As in the one-dimensional case, such solutions exist for discrete values of the asymptotic wave number (or equivalently, the frequency of oscillation of the entire solution). For target patterns, we construct solutions for a sequence of frequencies. For spirals, we construct only the “lowest mode” solution. 相似文献
Full-size image
17.
Evsey Dyn'kin 《Journal of Approximation Theory》1997,91(3):349-367
A new hyperbolic area estimate for the level sets of finite Blaschke products is presented. The following inversion of the usual Sobolev embedding theorem is proved:
Hereris a rational function of degreenwith poles outside
. This estimate implies a new inverse theorem for rational approximation of analytic functions with respect to areaLpnorm. 相似文献
Full-size image
18.
We study best uniform approximation of periodic functions from
where the kernelK(x, y) is strictly cyclic variation diminishing, and related problems including periodic generalized perfect splines. For various approximation problems of this type, we show the uniqueness of the best approximation and characterize the best approximation by extremal properties of the error function. The results are proved by using a characterization of best approximants from quasi-Chebyshev spaces and certain perturbation results. 相似文献
Full-size image
19.
Tams Erdlyi 《Journal of Approximation Theory》2001,112(2):171
Let Λ(λj)∞j=0 be a sequence of distinct real numbers. The span of {xλ0, xλ1, …, xλn} over
is denoted by Mn(Λ)span{xλ0, xλ1, …, xλn}. Elements of Mn(Λ) are called Müntz polynomials. The principal result of this paper is the following Markov-type inequality for products of Müntz polynomials. T
2.1. LetΛ(λj)∞j=0andΓ(γj)∞j=0be increasing sequences of nonnegative real numbers. Let
Then
18(n+m+1)(λn+γm).In particular ,
Under some necessary extra assumptions, an analog of the above Markov-type inequality is extended to the cases when the factor x is dropped, and when the interval [0, 1] is replaced by [a, b](0, ∞). 相似文献
Full-size image
Full-size image
Full-size image
20.
Given α (0, 1), let Tα be the Carleson class of all meromorphic maps ƒ from the unit disk
to the extended complex plane
with
where ƒ# and dm mean the spherical derivative of ƒ and Lebesgue area measure on
separately. And, let BITα and BITα,0 be the biholomorphically invariant families (amongst the Carleson class) consisting of those ƒ Tα with sup
and lim|w| → 1 ||ƒ ο φw||Tα = 0 respectively, where. The main purpose of this article is to study BITα and BITα,0 via the Ahlfors-Shimizu characteristic, canonical factorization and bounded holomorphic maps. 相似文献
Full-size image