共查询到20条相似文献,搜索用时 12 毫秒
1.
A. M. Sedletskii 《Mathematical Notes》2006,79(5-6):697-706
Let g be a given function in L 1 = L 1(0, 1), and let B be one of the spaces L p (0, 1), 1 ≤ p < ∞, or C 0[0, 1]. We prove that the set of all convolutions f * g, f ∈ B, is dense in B if and only if g is nontrivial in an arbitrary right neighborhood of zero. Under an additional restriction on g, we prove the equivalence in B of the systems f n * g and I f n , where f n ∈ L 1, n ∈ ?, and I f = f * 1 is the antiderivative of f. As a consequence, we obtain criteria for the completeness and basis property in B of subsystems of antiderivatives of g. 相似文献
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We consider settings in convex analysis which give rise to families of convex functions that contain their lower envelope. Given certain partial data regarding a subdifferential, we consider the family of all convex antiderivatives that comply with the given data. We prove that this family is not empty and, in particular, contains a minimal antiderivative under a fairly general assumption on the given data. It turns out that the representation of monotone operators by convex functions fits naturally in these settings. Duality properties of representing functions are also captured by these settings, and the gap between the Fitzpatrick function and the Fitzpatrick family is filled by this broader sense of minimality of the Fitzpatrick function. 相似文献
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Having studied families of antiderivatives and their envelopes in the setting of classical convex analysis, we now extend and apply these notions and results in settings of abstract convex analysis. Given partial data regarding a c-subdifferential, we consider the set of all c-convex c-antiderivatives that comply with the given data. Under a certain assumption, this set is not empty and contains both its lower and upper envelopes. We represent these optimal antiderivatives by explicit formulae. Some well known functions are, in fact, optimal c-convex c-antiderivatives. In one application, we point out a natural minimality property of the Fitzpatrick function of a c-monotone mapping, namely that it is a minimal antiderivative. In another application, in metric spaces, a constrained Lipschitz extension problem fits naturally the convexity notions we discuss here. It turns out that the optimal Lipschitz extensions are precisely the optimal antiderivatives. This approach yields explicit formulae for these extensions, the most particular case of which recovers the well known extensions due to McShane and Whitney. 相似文献
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We derive algorithms which permit the inspection of plane hole patterns for their position tolerance. The entire hole pattern is measured by a coordinate measuring machine and then is fitted into the nominal pattern in such a way as to minimize the maximum of the distances between the nominal and the actual positions.
Zusammenfassung Wir entwickeln Algorithmen, mit deren Hilfe die Einhaltung der Positionstoleranzen ebener Lochbilder untersucht werden kann. Die Gruppe der Ist-Zentren wird dabei gegenüber der Gruppe der Soll-Zentren so eingepaßt, daß der maximale Abstand zwischen den Soll- und den Ist-Werten minimal ausfällt.相似文献
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V. Totik 《Analysis Mathematica》1982,8(2):151-163
слЕДУь п. к. сИккЕМА, Мы ИсслЕДУЕМ АппРОксИМ АцИОННыЕ сВОИстВА ОпЕРАтОРОВ $$u_\varrho ^\beta (f,x) = \frac{1}{{\beta _\varrho }}\int\limits_{ - \infty }^\infty {f(x - t)\beta ^\varrho (t) dt(\varrho \to \infty ).} $$ жДЕсьΒ — НЕОтРИцАтЕл ьНАь сУММИРУЕМАь ФУН кцИь, \(\beta _\varrho = \int\limits_{ - \infty }^\infty {\beta ^\varrho (t) dt} \) И ВыпОлНЕНы УслОВИь: (i)Β(0)=1 ИΒ НЕпРЕРыВНА В тО ЧкЕt=0, (ii) \(\mathop {\sup }\limits_{\left| t \right| > \delta } \beta (t)< 1\) Дль кАжДОгОδ>0. ДОкАжАНО, ЧтО ЁкспОНЕ НцИАльНыИ пОРьДОк Ап пРОксИМАцИИ МОжЕт Быть ДОстИгНУт тОлькО Дль ФУНкцИИ ВИДА (fx)=ax+b И (fx)=ae bx+c. ЁтО — ИсклУЧИтЕльНыЕ слУЧАИ, пОскОлькУ УкАжАННыЕ ФУНкцИИ ьВ льУтсь ЕДИНстВЕННыМ И НЕпОДВИжНыМИ тОЧкАМ И Дль ОпЕРАтОРОВU β ? . ДОкАжАНО тАкжЕ, ЧтО пР И УДАЧНОМ ВыБОРЕΒ МО жНО ДОБИтьсь «пОЧтИ Ёксп ОНЕНцИАльНОгО» пОРьДкА АппРОксИМАц ИИ. НАкОНЕц, В пОслЕДНЕИ т ЕОРЕМЕ УтВЕРжДАЕтсь, ЧтО сУЩЕстВУУт тАкИЕΒ Иf, ЧтОU β ? (f,x) пРИp→∞ РАсхОДьтсь НА МНОжЕстВЕ пОлОжИтЕл ьНОИ МЕРы. 相似文献
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S. Fridli 《Acta Mathematica Hungarica》1986,47(1-2):33-44
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The subject of this paper is to study the problem of the approximation of function of two variables by means of Chlodowsky-Taylor polynomials in a rectangular domain. 相似文献
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We show that the complexity of a parabolic or conic spline approximating a sufficiently smooth curve with non-vanishing curvature
to within Hausdorff distance ɛ is c
1ɛ−1/4 + O(1), if the spline consists of parabolic arcs, and c
2ɛ−1/5 + O(1), if it is composed of general conic arcs of varying type. The constants c
1 and c
2 are expressed in the Euclidean and affine curvature of the curve. We also show that the Hausdorff distance between a curve
and an optimal conic arc tangent at its endpoints is increasing with its arc length, provided the affine curvature along the
arc is monotone. This property yields a simple bisection algorithm for the computation of an optimal parabolic or conic spline.
The research of SG and GV was partially supported by grant 6413 of the European Commission to the IST-2002 FET-Open project
Algorithms for Complex Shapes in the Sixth Framework Program. 相似文献
15.
A discrete, positive, weighted algebraic polynomial operator which is based on Gaussian quadrature is constructed. The operator is shown to satisfy the Jackson estimate and an optimal version is obtained. 相似文献
16.
Peter P. Varju 《Constructive Approximation》2007,26(3):317-337
Let
be the boundary of a convex domain symmetric to the origin. The conjecture that any continuous even function can be uniformly
approximated by homogeneous polynomials of even degree on K is proven in the following cases: (a) if d = 2; (b) if K is twice
continuously differentiable and has positive curvature in every point; or (c) if K is the boundary of a convex polytope. 相似文献
17.
《Journal of Computational and Applied Mathematics》1999,102(1):143-156
Given a surface or scattered data points from a surface in 3-space, we show how to approximate the given data by a ruled surface in tensor product B-spline representation. This leads us to a general framework for approximation in line space by local mappings from the Klein quadric to Euclidean 4-space. The presented algorithm for approximation by ruled surfaces possesses applications in architectural design, reverse engineering, wire electric discharge machining and NC milling. 相似文献
18.
Boris I. Kvasov 《Numerical Algorithms》2001,27(2):169-188
This paper addresses the definition and the study of discrete generalized splines. Discrete generalized splines are continuous piecewise defined functions which meet some smoothness conditions for the first and second divided differences at the knots. They provide a generalization both of smooth generalized splines and of the classical discrete cubic splines. Completely general configurations for steps in divided differences are considered. Direct algorithms are proposed for constructing discrete generalized splines and discrete generalized B-splines (discrete GB-splines for short). Explicit formulae and recurrence relations are obtained for discrete GB-splines. Properties of discrete GB-splines and their series are studied. It is shown that discrete GB-splines form weak Chebyshev systems and that series of discrete GB-splines have a variation diminishing property. 相似文献
19.
Hermann Knig 《Mathematische Nachrichten》1993,162(1):125-138
Results on the degree of approximation of continuous or Lipschitz-continuous functions f:Sn?1 → ? on the sphere in ?n by spherical functions of degree k are given in terms of k and n, strengthening results of Newman and Shapiro. An example of (restriction of) a norm shows the result to be the best possible in k and n. Further, results for smoother functions are discussed. 相似文献
20.
In this paper, a number of problems concerning the uniform approximation of complex-valued continuous functions
on compact subsets of the complex plane by simplest fractions of the form
are considered. In particular, it is shown that the best approximation of a function
by the fractions
is of the same order of vanishing as the best approximations by polynomials of degree
. 相似文献