共查询到20条相似文献,搜索用时 15 毫秒
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M. Ounaïes 《Journal of Geometric Analysis》2007,17(4):701-715
We use L2 estimates for the
equation to find geometric conditions on discrete interpolating varieties for weighted spaces Ap(ℂ) of entire functions such that |f(z)|≤AeBp(z) for some A, B>0. In particular, we give a characterization when p(z)=e|z| and more generally, when In p(er) is convex andIn p(r) is concave.
Acknowledgements and Notes. The author wishes to thank X. Massaneda for useful talks and remarks. 相似文献
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A. I. Shapovalov 《Mathematical Notes》2000,67(4):523-533
A generalization of the Taylor expansions of entire functions with variable center is used to illustrate the notion of conjugate interpolation problem. The radii of existence, uniqueness, and convergence for such problems are found. A relationship between the interpolation functional systems of two mutually conjugate problems is revealed. Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 616–628, April, 2000. 相似文献
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We prove that, under suitable assumptions, an isomorphism g of dense subsets A,B of the real line can be taken to approximate a given increasing Cn surjection f with the derivatives of g agreeing with those of f on a closed discrete set. For example, we have the following theorem. Let be a nondecreasing Cn surjection. Let be a positive continuous function. Let be a closed discrete set on which f is strictly increasing. Let each of {Ai}, {Bi} be a sequence of pairwise disjoint countable dense subsets of such that for each and xE we have xAi if and only if f(x)Bi. Then there is an entire function such that and the following properties hold.
- (a) For all , Dg(x)>0.
- (b) For k=0,…,n and all , |Dkf(x)−Dkg(x)|<ε(x).
- (c) For k=0,…,n and all xE, Dkf(x)=Dkg(x).
- (d) For each , g[Ai]=Bi.
Keywords: Order-isomorphism; Second category; Entire function; Oracle-cc forcing; Complex approximation; Interpolation; Hoischen's theorem 相似文献
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Necessary density conditions for sampling and interpolation of certain entire functions 总被引:1,自引:0,他引:1
H. J. Landau 《Acta Mathematica》1967,117(1):37-52
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A. K. Varma 《Acta Mathematica Hungarica》1978,31(3-4):193-203
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A. K. Varma 《Acta Mathematica Hungarica》1978,31(3-4):185-192
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《Journal of Computational and Applied Mathematics》1997,80(1):97-104
The interpolation of a discrete set of data on the interval [0, 1], representing the first and the second derivatives (except at 0) of a smooth function f is investigated via quartic C2-splines. Error bounds in the uniform norm for ∥s(i) − f(i)∥, i=0(1)2, if f ∈ Cl[0, 1], l=3, 5 and (3) ∈ BV[0, 1], together with computational examples will also be presented. 相似文献
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Research supported by the Norwegian Research Council for Science and Humanities (NAVF). 相似文献
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On the trigonometric interpolation and the entire interpolation 总被引:17,自引:0,他引:17
Liu Yongping 《分析论及其应用》1990,6(4):85-106
In this paper, we study a kind of interpolation problems on a given nodal set by trigonometric polynomials of order n and
entire functions of exponential type according as the nodal set is
respectively. We established some equivalent conditions and found the explicit forms of some interpolation functions on the
interpolation problems. As a special case, the explicit forms of fundamential functions of (0,m)-interpolat on by trigonometric
case or entire functions case (in B2
σ) respectively, if they exist, may follow from our results. Besides, we also considered the convergence of the interpolation
functions at above stated.
Suported by the Natural Youth Science Foundation of Beijing Normal University. 相似文献
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