共查询到20条相似文献,搜索用时 31 毫秒
1.
Vesselin Vatchev 《分析论及其应用》2011,27(2):187-200
For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln(ψ) = n ∑ k=0 akψ(k), where the constant coefficients ak ∈ R may be adapted to f . We prove that for each f ∈ C(n)(I), there is a selection of coefficients {a1, ,an} and a corresponding linear combination Sn( f ,t) = n ∑ k=1 bkeλkt of functions ψk(t) = eλkt in the nullity of L which satisfies the following Jackson’s type inequality: f (m) Sn(m )( f ,t) ∞≤ |an|2n|Im|1/1q/ep|λ|λn|n|I||nm1 Ln( f ) p, where |λn| = mka x|λk|, 0 ≤ m ≤ n 1, p,q ≥ 1, and 1p + q1 = 1. For the particular operator Mn(f) = f + 1/(2n) f(2n) the rate of approximation by the eigenvalues of Mn for non-periodic analytic functions on intervals of restricted length is established to be exponential. Applications in algorithms and numerical examples are discussed. 相似文献
2.
设 {ε,εt;t∈ Z}是 iid的 B值随机变量序列 ,{ aj;j∈ Z}是一个实数列 ,满足 ∞j=-∞|aj|<∞ .记 Xt= ∞j=-∞ajεt-j,Sn = nt=1Xt.对 p≥ 1 ,本文研究了n-1 -( p/ 2 ) (2 L2 n) -( p/ 2 ) ni=1 ‖ Si‖p 及 n-1 -( p/ 2 ) (2 L2 n) -( p/ 2 ) ni=0 ‖ Sn- Si‖ p的渐进性质 ,使得 Strassen(1 964)及 Chen(1 994)的一些结果得到推广 . 相似文献
3.
<正> 以fk(z)表單位圓內的K次對稱單葉全純函數,亦即fk(z)=z+a_I~((k))z~(k+1)+a_2~((k))z~(2k+1)+…,|z|<1.以S_k表此種函數之全體.特別,書S以代S_1. 相似文献
4.
<正> 1.设 p 次对称函数(?)在单位圆|z|<1中是正则的单叶的,此种函数的全体成一函数族 S_p.当p=1时,简讯 S_1为 S.设ω=f(z)∈S_p 映照|z|<1于 W 面上时,其像关于原点成星形,此种 f(z)成 S_p 之一子族S_p.设 f(z)∈S_p, 相似文献
5.
For Vilenkin-like system, the authors define a new operator H*f := supn |Hnf|, where Hnf is the weighted average for partial sums, and prove that H* is of type (Hp* (Gm), Lp(Gm)) for all 1/2 < p ≤∞. As a consequence, the authors prove the operator S*f := supn |Snf| is of type (p, p) for 1 < p < ∞, where Snf is the n-partial sum. 相似文献
6.
Tomasz Beberok 《Journal of Geometric Analysis》2016,26(4):2883-2892
In this paper we obtain the closed forms of some hypergeometric functions. As an application, we obtain the explicit forms of the Bergman kernel functions for Reinhardt domains \(\{|z_3|^{\lambda } < |z_1|^{2p} + |z_2|^2, \ |z_1|^{2p} + |z_2|^2 < |z_1|^{p} \}\) and \(\{|z_4|^{\lambda } < (|z_1|^2 + |z_2|^2)^{p} + |z_3|^2, \ (|z_1|^2 + |z_2|^2)^{p} + |z_3|^2 < (|z_1|^2 + |z_2|^2 )^{p/2} \}\). 相似文献
7.
Sun Xiehua 《数学年刊B辑(英文版)》1987,8(4):468-470
To answer the rest part of the problem of Boas R. P. on derivative of polynomial, it is shown that if $\[p(z)\]$ is a polynomial of degree n such that $\[\mathop {\max }\limits_{\left| z \right| \le 1} \left| {p(z)} \right| \le 1\]$ and $\[{p(z) \ne 0}\]$ in $\[\left| z \right| \le k,0 < k \le 1\]$, then $\[\left| {{p^''}(z)} \right| \le n/(1 + {k^n})\]$ for $\[\left| z \right| \le 1\]$. The above estimate is sharp and the equation holds for $\[p(z) = ({z^n} + {k^n})/(1 + {k^n})\]$. 相似文献
8.
1.:敲g(x)篇〔一二,二]上之非降的有界缝差两数,业具有性鬓(K)s‘二一0,一。(:);f--:.,。g。尹(:)!d:一郁匕,(‘一”,”;dg)篇在〔一二,司上定羲业且满足修件:,一{户,(柳dg(·)}青<一,>l的可测蝮值函数族{f(幻}.封龄一徊乙“(一二,侧d刃中之子族凌B(幻},若由f(劣)(乙,(一二,二:dg),夕>1生+上夕q=1,及f--:ha”“’“““’一0纷{B(x)}之任何B(哟成立必滇致f(幻在〔一二,司上规乎虚虚等焚零则释{B(x)}在乙“(一二,侧dg)中完全. 函数族的完全性是舆函数横造的一些简题很有阴保的.徙【l]我们知道{e‘”}豁。是在乙,(一二,州dg),,>1,中完全的,… 相似文献
9.
Charles S. Kahane 《Integral Equations and Operator Theory》1984,7(1):96-117
The integral operator which sends f (ζ) into $$\int_{|\xi |< 1} {\tfrac{{f(\xi )}}{{|x - \xi |^{p - 1} }}} d\xi = g(x)(|x|< 1)$$ x and ζ ∈ RP, is shown to map the space of functions f (ζ) on |ζ|<1, square integrable with respect to the weight (1-|ξ|2)1/2 one to one onto the space of functions g (x) on |x|<1 which possess gradients δg(x) in the sense of distribution theory, with both g(x) and δg(x) being square integrable with respect to the weight (1-|x|2)1/2. This extends to p≥3 a result of P. Wolfe's in the case p=2. 相似文献
10.
劳勃生的特殊星像函数和特殊凸像函数 总被引:6,自引:1,他引:6
<正> 设函数w在单位圆 E_z:|z|<1上是正则的.假如f(z)在 E_z上是单叶的,那末 D_f=f(E_z)是 w 平面上单叶的区域.记这种单叶函数f(z)的全体为 S_p,S_1=S.若 D_f 以原点 w=0 为星形中心,就是说若 w_0∈D_f则缐段■整个地落在区域 D_f 中,称这种函数 f(z)是 E_z 中的星像函数,其特徵是在 E_z 相似文献
11.
On the Radial Ground State of p-Laplacian Equation Involving Super-critical or Critical Exponents
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In this paper, we consider the existence and uniqueness of the radial ground state to the following p-Laplacian equation involving super-critical or critical exponents: Δ_pu + u^q - |Du|^σ = 0, x ∈ R^n, 2 ≤ p < n, q ≥ [n(p - 1) + p]/(n - p), σ > 0. Applying the shooting argument, the Schauder's fixed point theorem and some delicate estimates of auxiliary functions, we study the influence of the parameters n, p, q, σ on the existence and uniqueness of the radial ground state to the above p-Laplacian equation. 相似文献
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13.
重新确定了广义超特殊p-群G的自同构群的结构.设|G|=p~(2n+m),|ζG|=p~m,其中n≥1,m≥2,Aut_cG是AutG中平凡地作用在ζG上的元素形成的正规子群,则(i)若p是奇素数,则AutG=〈θ〉×Aut_cG,其中θ的阶是(p-1)p~(m-1);若p=2,则AutG=〈θ_1,θ_2〉×Aut_cG,其中〈θ_1,θ_2〉=〈θ_1〉×〈θ_2〉≌Z_(2m-2)×Z_2.(ii)如果G的幂指数是p~m,那么Aut_cG/InnG≌Sp(2n,p).(iii)如果G的幂指数是p~(m+1),那么Aut_cG/InnG≌K×Sp(2n-2,p),其中K是p~(2n-1)阶超特殊p-群(若p是奇素数)或者初等Abel 2-群.特别地,当n=1时,Aut_cG/InnG≌Z_p. 相似文献
14.
Let Ap(n)(p, n∈N={1,2,...}) denote the class of functions of the form f(z)=zp+ap+nzp+n+... which are analytic in the unit disc E={z:|z|<1}. By using the method of differential subordinations we give some sufficient conditions for a function f(z)∈Ap(n) to be a certain subclass Rp(n,k) of p-valently close-to-convexity functions. 相似文献
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17.
N. K. Govil 《分析论及其应用》1989,5(3):79-82
A well-known theorem of Ankeney and Rivlin states that if p(z) is a polynomial of degree n, such that p(z)≠0 for |z|<1, then
. In this paper we improve this bound. 相似文献
18.
Bernoulli and Euler polynomials are considered for large values of the order. Convergent expansions are obtained for B n ( nz +1/2) and E n ( nz +1/2) in powers of n −1 , and coefficients are rational functions of z and hyperbolic functions of argument 1/(2 z ). These expansions are uniformly valid for | z ± i /2π|>1/2π and | z ± i /π|1/π, respectively. For a real argument, the accuracy of these approximations is restricted to the monotonic region. The range of validity of the uniformity parameter z is enlarged, respectively, to regions of the form | z ± i /2( m +1)π|>1/2( m +1)π and | z ± i /(2 m +1)π|>1/(2 m +1)π, m =1,2,3,…, by adding certain combinations of incomplete gamma functions to these uniform expansions. In addition, the convergence of these improved expansions is stronger, and for a real argument, the accuracy of these improved approximations is also better in the oscillatory region. 相似文献
19.
利用非光滑临界点理论 ,本文证明了一类临界增长非线性椭圆方程-div(A(x ,u) | u|p-2 u) 1pA′u(x ,u) | u|p =g(x ,u) |u|p -2 u ,u=0 , Ω ; Ω 非平凡正解的存在性 .其中 1
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20.
Let
. The present note gives the asymptotoc formula of max
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This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献