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1.
用B_(δ,p)(1P∞)表示P次可积Fourier变換具有紧支集[-δ,δ]的带有限函数。证明了对于B_(3δ,p)中的函数,可以在L_p(R)尺度下,由序列{f(κπ/δ)},{f'(κπ/δ)}以及{f'(κπ/δ)}的Hermite型插值进行重构.  相似文献   

2.
任意的无理数x,其无理指数δx∶=sup{δ≥0∶|x-pq-1|≤q-2δi.o.pq-1}衡量x可以被有理数逼近的程度.经典的Jarník-Besicovitch定理表明,对于任意的δ≥1,集合{x∈R∶δx≥δ}的Hausdorff维数为δ-1.Barral和Seuret[1]考虑该定理的局部化问题,证明对于任意的连续函数f∶R→[1,+∞),集合{x∈R∶δx≥f(x)}的Hausdorff维数为(inf{f(x)∶x∈R})-1.本文从经典的Jarník-Besicovitch定理出发,利用连分数的理论给出局部Jarník-Besicovitch定理一个简短的证明.  相似文献   

3.
In this paper, we characterize BMOA and VMOA on the unit ball in terms of normsNp(f)=sup/x∈B{1/σ(Q(z))∫Q(z)│f(ξ)-f(z)│pdσ(ξ)}^1/p,1≤p&;lt;∞ and more general Garcia norms.Where Q(z)=Q(n(z),δz)={ξ∈S,│^1/2&;lt;δZ}.n(z)={e1,z=0,/z/│z│,z=0,δz=[2(1-│z│)]^1/2.  相似文献   

4.
主要证明了:设f(z)于开平面上超越亚纯,0δ1,且lim—r→∞(logT(r+1/r,f)/logT(r,f))+∞,则存在一列复数a_n(n=1,2,…),使集合{a:△_1)(a,f)δ}含于∩∞j=1∪∞n=j﹛a:|a-an|e-enσ﹜,其中σ=(log2/2-δ)/2([10/δ])0.即{a:△_(1))(a,f)δ为一有穷μ测度集.  相似文献   

5.
葛洵  葛恒武 《大学数学》2014,30(5):48-50
解决了收敛数列连续函数保持性的一个逆问题.即对于f(D)中任一收敛数列y{n},必存在D中收敛数列{xn},使得{f(xn)}是y{n}的子数列,其中DR,f(x)是D上的闭连续函数.  相似文献   

6.
林群 《数学学报》1987,30(2):216-219
<正> 1972年A.Weitsman[1]证明对于下级有限的亚纯函数f(Z),有∑δ~(1/3)(a,f)<+∞,其中a是复数.本文在f(Z)是整函数的情况下,把这一结果推广到亏函数. 定理 设f(Z)是下级μ有限的整函数,则∑δ~(1/3)(a(Z),f)<+∞,其中a(Z)是满足T(r,a(Z))=o{T(r,f)}的亚纯函数.  相似文献   

7.
Suppose h∈L~2(R), α_0>1, b_0>0 and h_(mn) (x) =α_0~(-m/2)h(α_0~(-m)x - nb_0),m,n∈Zand suppose that {h_(mn)} is a frame with frame bounds A,B>0,where <·,·> is the standard inner product on L~2(R) and ||·|| is the L~2 norm on R .Wecall {h_(mn)} the affine frame. Denote its dual frame by {h_(mn)} .It is well known that forany f ∈L~2 (R),  相似文献   

8.
本文研究刻度参数分布族(1/σ)f(x/σ)中刻度参数在损失函数L(σ,δ)=(σ-δ)~2/σδ下的最小风险同变估计及其最小最大性。  相似文献   

9.
设σ是环R的一个自同态,δ是R的一个σ-导子.研究斜三角矩阵环Tn(R,α)的强可逆性和(σ,δ)-弱刚性,证明了1)若α是环R的一个刚性自同态,则环R是强可逆环当且仅当Tn(R,α)是强可逆环;2)若α和σ都是环R的刚性自同态,ασ=σα,且R是δ-弱刚性环,则R是(σ,δ)-弱刚性环当且仅当Tn(R,α)是(σ,δ)-弱刚性环.  相似文献   

10.
In this paper,we study the normality criterion for families of meromorphic functions concerning shared set depending on f∈F.Let F be a family of meromorphic functions in the unit disc A.For each f∈F,all zeros of f have multiplicity at least 2 and there exist nonzero complex numbers b_f,c_f satisfying(i) b_f/c_f is a constant;(ii) min{σ(0,b_f),σ(0,c_f),σ(b_f,c_f)} ≥m for some m 0;(iii) E_f'(S_f)■ E_f(S_f),where S_f = {b_f,c_f}.Then F is normal in A.At the same time,the corresponding results are also proved.The results in this paper improve and generalize the related results of[10-11]and  相似文献   

11.
LetB σ be the class of entire functions of exponential type σ, real valued and bounded in modulus by 1 in the real line. A setG of functions defined on the segment [-T-r, T+r], wherer is a fixed positive number, is called an (ε, δ)-net of the classB σ on the segment [-т, т] if for any f?B σ there existsg?G such that for anyx?[-T,T] $$\left| {f(x) - g(x)} \right| \leqq \frac{\varepsilon }{{2r}}\int\limits_{x - r}^{x + r} {\left| {f(t)} \right|dt + \delta .} $$ The main result consists in the following: For any positive σ, r, ε≦1, δ≦1 and sufficiently largeT we have $$H_{\varepsilon ,\delta } (B_\sigma ,T) \leqq \frac{{2\sigma T}}{\pi }\log \frac{{c(\sigma r)}}{{\max (\varepsilon ,\delta )}},$$ where c(σr) depends only on the product σr. The main tool of the proof of this inequality is the following estimate of the derivative of a polynomialP(x) with real coefficients: $$\left\| {P'(x)} \right\|_{L_p ( - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2},{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}) \leqq } c\left( {q + 1 + \sum\limits_{i = 1}^{n - q} {\frac{1}{{\left| {a_i } \right|^2 }}} } \right)\left\| {P(x} \right\|_{L_p ( - 1,1)} ,$$ whereq is the number of roots of the polynomialP(x) lying in the disk ¦z¦<1; a1, ..., an?g are the other roots, с is an absolute constant, and 1≦p≦∞.  相似文献   

12.
蘇步青 《数学学报》1956,6(3):374-388
<正> 本文是繼作者前篇論文之後的;目的在於詳細研究該文末節所論的關於拓廣的微小變形問題.和芬斯拉空間相類似地有E.Cartan所建立的以面積概念為基礎的  相似文献   

13.
Suppose f∈Hp(Tn), 0 r δ , δ=n/p?(n+1)/2. In this paper we eastablish the following inequality $$\mathop {\sup }\limits_{R > 1} \left\{ {\frac{1}{{\log R}}\int_1^R {\left\| {\sigma _r^\delta } \right\|_{H^p (T^R )}^p \frac{{dr}}{r}} } \right\}^{1/p} \leqslant C_{R,p} \left\| f \right\|_{H^p (T^R )} $$ It implies that $$\mathop {\lim }\limits_{R \to \infty } \frac{1}{{\log R}}\int_1^R {\left\| {\sigma _r^\delta - f} \right\|_{H^p (T^R )}^p \frac{{dr}}{r}} = 0$$ Moreover we obtain the same conclusion when p=1 and n=1.  相似文献   

14.
Let W: ?→(0,∞) be continuous. DoesW admit a classical Jackson Theorem? That is, does there exist a sequence $\{ \eta _n \} _{n = 1}^\infty $ of positive numbers with limit 0 such that for 1≤p≤∞, $\mathop {\inf }\limits_{\deg (P) \le n} ||(f - P)W||_{L_p (R)} \le \eta n||f'W||_{L_p (R)} $ for all absolutely continuousf with $||f'W||_{L_p (R)} $ finite? We show that such a theorem is true iff both $\mathop {\lim }\limits_{\chi \to \infty } W(\chi )\int_0^\chi {W^{ - 1} } = 0$ and $\mathop {\lim }\limits_{\chi \to \infty } W^{ - 1} (\chi )\int_\chi ^\infty W = 0,$ with analogous limits asx→?∞. In particular,W(x)=exp(?|x|) does not admit a Jackson theorem of this type. We also construct weights that admit anL 1 but not anL Jackson theorem (or conversely).  相似文献   

15.
On the classW r L p (1≦p≦∞;r=1, 2,…) of 1-periodic functions ?(x) having an absolutely continuous (r? l)st derivative such that $$\parallel f^{(r)} \parallel _{L_p } \leqq 1 (\parallel f^{(r)} \parallel _{L_\infty } = vrai \sup |f^{(r)} (x)|)$$ vrai sup ¦?(r)(x)¦) an optimal quadrature formula of the form (0 ≦? ≦r?1, 0 ≦x 0 < x1 <…< xm ≦ 1) is found in the cases ?=r?2 and ?=r? 3 (r=3, 5, …). An exact error bound is established for this formula. The statements proved forW r L p allowed us also to obtain, under certain restrictions posed on the coefficientsp kl, and the nodesx 0 andx m, optimal quadrature formulae for the classes $$W_0^r L_p = \{ f:f \in W^r L_p , f^{(i)} (0) = 0 (i = 0,1,...,r - 2)\} $$ and $$W_0^r L_p = \{ f:f \in \tilde W^r L_p , f^{(i)} (0) = f^{(i)} (1) = 0 (i = 0,1,...,r - 2)\} $$ for the same values ofp andr as above.  相似文献   

16.
Let a(n)be the Fourier coefficients of a holomorphic cusp form of weightκ=2n≥12 for the full modular group and A(x)=∑_(n≤x)a(n).In this paper,we establish an asymptotic formula of the fourth power moment of A(x)and prove that ∫T1A~4(x)dx=3/(64κπ~4)s_4;2()T~(2κ)+O(T~(2κ-δ_4+ε))with δ_4=1/8,which improves the previous result.  相似文献   

17.
韩忠月 《数学研究》2012,(3):250-262
研究一类高阶混合中立型微分方程:x(t)+ax(t-γ)-bx(t+σ)]~((m))+δ(q(t)x(t-g)+p(t)x(t+h))=0,其中a,b,γ,σ,g,h是正常数,P,q∈C(R~+,R~+),δ=士1,m≥1是整数.得到了方程振动的判据.  相似文献   

18.
We consider extensions of a total valuation ring V of a skew field K to the Ore extension K(X;σ, δ) for an endomorphism σ of K and a σ-derivation δ. It is shown that there exists an extension R of V with X ∈ R, such that ${\overline X}$ is transcendental over V/J(V) if and only if (σ,δ) is compatible with V, where ${\overline X} = X + J(R^(1))$ . In the case V is invariant, it is established that there is an invariant extension R of V in K(X;σ,δ) such that ${\overline X}$ is transcendental if and only if σ(a)V = aV and δ(a) ∈ aV for all a ∈ K.  相似文献   

19.
We reduce the boundedness of operators in Morrey spaces \(L_p^r\left( {\mathbb R}^n\right) \), its preduals, \(H^{\varrho }L_p ({\mathbb R}^n)\), and their preduals \(\overset{\circ }{L}{}^r_{p}\left( \mathbb {R}^n\right) \) to the boundedness of the appropriate operators in Lebesgue spaces, \(L_p({\mathbb R}^n)\). Hereby, we need a weak condition with respect to the operators which is satisfied for a large set of classical operators of harmonic analysis including singular integral operators and the Hardy-Littlewood maximal function. The given vector-valued consideration of these issues is a key ingredient for various applications in harmonic analysis.  相似文献   

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